John  Swett 


C^J  00 


ELEMENTS 


OF 


NATURAL     PHILOSOPHY 


FOR    THE    USE   OF 


anti 


BY 

J.   A.   GILLET, 

PROFESSOR  OF   PHYSICS    IX   THE   NORMAL  COLLEGE  OF  THE  CITY  OF  NEW  YORK, 
AND 

W.  J.    ROLFE, 

FORMERLY   HEAD   MASTER   OF   THE   HIGH   SCHOOL, 
CAMBRIDGE,    MASS. 


POTTER,    AINSWORTH,    &    CO. 

NEW   YORK   AND    CHICAGO. 
1884. 


Copyright,  1881, 
BY  J.    A     GtLLET  AND   W.   J.    ROLFE. 

SSUCAViiON  SEPT, 


Press  of  Rand,  Avery,  6°  Co.,  Boston. 


PREFACE. 


THIS  book  is  an  abridgment  of  the  "  Natural  Philos- 
ophy" by  the  same  authors,  with  such  changes  as  were 
required  to  adapt  it  to  younger  pupils.  As  the  larger 
book  is  in  no  sense  .a  revision  of  the  "  Natural  Philos- 
ophy"  of  the  "Cambridge  Course  of  Physics,"  but  an 
entirely  new  work,  differing  from  its  predecessor  both  in 
matter  and  in  method  of  presentation,  so  this  book  is 
equally  independent  of  the  earlier  "  Handbook  of  Natural 
Philosophy." 

Two  kinds  of  type  have  been  used,  as  in  the  larger 
book,  with  a  view  to  adapting  it  to  the  wants  of  different 
schools.  The  matter  in  the  larger  type  forms  a  brief  and 
easy  course,  complete  in  itself  and  sufficient  for  classes 
that  can  spend  only  a  single  school  term  in  the  study. 
The  portions  in  smaller  type  will  enable  teachers  to 
extend  this  course  more  or  less,  according  to  their  per- 
sonal tastes  or  the  ability  of  their  pupils.  Those  who 
have  time  for  the  whole  book  may  find  the  division  con- 
venient in  reviews  and  examinations,  and  also  in  fixing 
the  minimum  to  be  required  of  pupils  who  have  little 
taste  or  aptitude  for  physics. 


iv  PREFACE. 

The  authors  have  carefully  avoided  doing  an  tvie 
teacher's  work  for  him  by  anticipating  every  familiar 
illustration  which  he  Would  either  give  his  pupils  orally 
or  lead  them  to  see  and  state  for  themselves.  Teachers 
may  be  supposed  to  know  something,  and  it  is  a  very 
dull  pupil  that  knows  nothing  at  all,  except  what  is  "  in 
the  book."  Both  teacher  and  pupil  become  mere  ma- 
chines when  the  one  has  only  to  hear  the  other  repeat 
what  he  has  learned  by  rote  from  the  printed  page.  Such 
practical  hints  and  suggestions  as  may  be  needed  by  the 
young  and  inexperienced  instructor  had  better  be  fur- 
nished him  outside  of  the  text-book. 

It  may  be  added  that  the  hook  of  which  this  is  an 
abridgment  will  be  useful  in  various  ways  to  the  teacher 
of  this  ;  and  he  will  also  get  much  help  from  any  of 
the  following  works,  to  which  the  authors  have  already 
acknowledged  their  indebtedness  in  che  preface  to  the 
larger  book :  — 

Baseband's  Natural  Philosophy.      D.  Appleton  &  Co. :  New 

York  (reprint). 

Ganotfs  Physics.     Wm.  Wood  &  Co.  :   New  York  (reprint). 
Tait's    Recent  Advances  in  Physical  Science.      Macmillan  & 

Co. :   New  York. 

Maxwell's  Matter  and  Motion.     Macmillan  &  Co.  :  New  York. 
Tyndall's  Sound.     D.  Appleton  &  Co.  :   New  York  (reprint). 
Mayer's  Sound.     D.  Appleton  &  Co.  :  New  York. 
Helmholtz's    Popular    Lectures.     1st  Series.     D.   Appleton  £ 

Co.  :   New  York  (reprint). 

Taylor's  Sound  and  Music.    Macmillan  £  Co.  :  New  York. 
TyndalFs  Heat  a  Mode  of  Motion.     D.  Appleton  &  Co.  :  New 

York  (reprint). 
Maxwell's  Theory  of  Heat.     D.  Appleton  &  Co. :  New  York 

(reprint). 
Mayer's  Light.     D.  Appleton  £  Co.  :  New  York. 


PREFACE.  V 

Tyndall's  Lectures  on  Light.  D.  Appleton  &  Co. :  New  York. 
Rood's  Modern  Chromatics.  D.  Appleton  &  Co.  :  New  York. 
Jeffries's  Color  Blindness.  Houghton,  Mifflin,  &  Co. :  Boston. 
Gordon's  Electricity  and  Magnetism.  D.  Appleton  &  Co.  : 

New  York  (reprint). 
Jenkin's   Electricity  and  Magnetism.      D.    Appleton  &    Co.  ; 

New  York  (reprint). 
Tyndall's  Lessons  in  Electricity.     D.   Appleton  &  Co.:  New 

York  (reprint). 

Prescott's  Telegraph.     D.  Appleton  &  Co. :   New  York. 
Prescott's  Telephone,  etc.     D.  Appleton  &  Co.:  New  York. 
Sawyer's  Electric  Lighting.     D.  Van  Nostrand  :  New  York. 
Loomis's  Meteorology.     Harper  &  Brothers  :   New  York. 
Stewart's  Energy.     D.  Appleton  &  Co.  :  New  York. 


CONTENTS. 


I.  CONSTITUTION   OF   MATTER i 

II.  MECHANICS 5 

A.  DEFINITIONS.  —  UNITS.  —  NEWTON'S  LAWS  OF  MO- 

TION      5 

B.  WORK  AND  ENERGY 17 

C.  COMPOSITION  AND  RESOLUTION  OF  FORCES      ...  20 

D.  GRAVITY  AND  EQUILIBRIUM 23 

E.  FALLING  BODIES 30 

F.  THE  PENDULUM 36 

G.  MACHINES 39 

III.  PHYSICS 53 

I.  STATES  OF  MATTER 53 

A.  THREE  STATES  OF  MATTER 53 

B.  FLUIDS 55 

C.  GASES 63 

D.  LIQUIDS  .  • 69 

E.  SOLIDS 90 

II.  SOUND     . 93 

A.  ORIGIN  OF  SOUND 93 

B.  PROPAGATION  OF  SOUND 96 

C.  RESONANCE 104 

D.  MUSICAL  INSTRUMENTS 106 

E.  THE  HUMAN  EAR 112 

III.  HEAT 114 

I.  EFFECTS  OF  HEAT 114 

A.  EXPANSION 114 

B.  MEASUREMENT  OF  TEMPERATURE 119 


Vlll  CONTENTS. 

PAGE 

C.  CHANGE  OF  STATE 123 

I.  FUSION  AND  SOLIDIFICATION 123 

II.  EVAPORATION  AND  CONDENSATION    ....  125 

D.  MEASUREMENT  OF  HEAT 131 

II.  RELATIONS  BETWEEN  HEAT  AND  WORK 134 

III.  DISTRIBUTION  OK  HEAT 139 

A.  CONDUCTION 139 

B.  CONVECTION 143 

C.  RADIATION  AND  ABSORPTION 143 

IV.  LIGHT 149 

A.  RADIATION 149 

B.  REFLECTION 156 

C.  REFRACTION 158 

D.  DISPERSION 161 

E.  LENSES 165 

F.  OPTICAL  INSTRUMENTS 173 

G.  COLOR 185 

V.  MAGNETISM 192 

VI.  ELECTRICITY 201 

I.  FRICTIONAL  ELECTRICITY 201 

A.  ELECTRICAL  ATTRACTIONS  AND  REPULSIONS  .    .  201 

B.  ELECTRICAL  CONDUCTION  AND  INSULATION    .    .  204 

C.  ELECTRICAL  INDUCTION 205 

D.  ELECTRICAL  POTENTIAL 209 

E.  ELECTRICAL  CHARGE  AND  DISCHARGE     ....  210 

II.  VOLTAIC  ELECTRICITY 221 

A.  DEFLECTION  OF  THE  NEEDLE 221 

B.  FLOW  OF  ELECTRICITY  THROUGH  CONDUCTORS    .  224 

C.  ELECTRO-CHEMICAL  ACTION 226 

I.  VOLTAIC  BATTERIES 226 

II.  ELECTROLYSIS 232 

D.  ELECTRO-MAGNETIC  INDUCTION 234 

E.  TELEGRAPHY 242 

F.  TRANSMISSION  OF  POWER  BY  MEANS  OF  ELECTRI- 

CITY      251 

G.  ELECTRO-THERMAL  ACTION 252 

VII.  METEOROLOGY 257 

I.  CONSTITUTION  OF  THE  ATMOSPHERE     .....  257 

II.  TEMPERATURE  OF  THE  ATMOSPHERE 260 

III.  HUMIDITY  OF  THE  ATMOSPHERE 268 

IV.  MOVEMENTS  OF  THE  ATMOSPHERE 270 

V.  CONDENSATION  IN  THE  ATMOSPHERE 277 

A.  DEW  AND  HOAR-FROST 277 


CONTENTS. 

PAGE 

B.  FOG  AND  MIST 279 

C.  CLOUDS  AND  RAIN 2Sl 

D.  STORMS : 

VI.  ELECTRICAL  PHENOMENA  OF  THE  ATMOSPHERE  .    .  292 

A.  ATMOSPHERIC  ELECTRICITY 292 

B.  LIGHTNING 293 

C.  THE  AURORA 296 

VII.  OPTICAL  PHENOMENA  OF  THE  ATMOSPHERE    ...  298 

A.  REFRACTION 298 

B.  REFLECTION 3°3 

C.  CORONA  AND  HALOS 3°5 

VIII.  THE  THREE  GREAT  CIRCULATIONS  OF  THE  GLOBE  307 


ELEMENTS 


OF 


NATURAL     PHILOSOPHY. 


ELEMENTS 

OF 

NATURAL    PHILOSOPHY. 


i. 

CONSTITUTION   OF   MATTER. 

1.  Molecules  and  Atoms. — All  bodies  are  supposed  to 
be  made  up  of  very  small  particles,  called  molecules,  which 
are  in    turn    made    up    of    still    smaller    particles,    called 
atoms. 

These  molecules  are  far  too  minute  to  be  seen  with  the  most 
powerful  microscope,  and  are  separated  by  spaces  many  times 
as  large  as  the  molecules  themselves.  It  has  been  estimated 
that  there  are  at  least  300  quintillions  of  molecules  in  one  cubic 
inch  of  air,  —  a  number  which  would  be  represented  by  3  fol- 
lowed by  twenty  ciphers.  At  the  same  time  it  is  believed  that 
the  material  molecules  themselves  occupy  only  ¥^¥  of  the  space 
in  the  cubic  inch.  The  atoms  that  make  up  the  molecules  are 
also  believed  to  be  very  far  apart  compared  with  their  size.  We 
thus  gain  some  notion  of  the  extreme  fineness  of  the  atomic  dust 
of  which  matter  is  composed. 

We  can  resolve  bodies  into  molecules,  and  molecules 
into  atoms ;  but  it  has  not  been  found  possible  to  divide 
the  atoms. 

2.  Substance. — The  substance  of  a  body  depends  upon 
the  internal  structure  of  its  molecules.     All  the  molecules  of 
the  same  substance  are  supposed  to  be  exactly  alike.     A 

i 


ELEMENTS   OF 


c  t)6dy  may^ t>e  divided  and  subdivided  at  will,  and  the  sub- 
stance of  every  portion  will  remain  the  same  so  long  as  the 
molecules  are  unchanged.  If  the  molecules  are  divided, 
or  their  structure  is  altered  by  changing  the  kind,  number, 
or  grouping  of  their  atoms,  the  substance  of  the  body  is 
changed. 

If  a  piece  of  iron  is  reduced  to  the  finest  powder,  every  parti- 
cle is  iron  still ;  but  if  the  iron  rusts,  its  molecules  unite  with 
those  of  oxygen  in  the  air,  forming  more  complex  molecules  and 
a  new  substance.  Ice  may  be  changed  to  water,  and  water  to 
steam,  without  change  of  substance,  for  the  molecules  remain 
the  same  ;  but  if  we  divide  these  molecules  by  chemical  pro- 
cesses we  obtain  oxygen  and  hydrogen,  two  substances  made 
up  of  less  complex  molecules. 

3.  The  Ether.  —  A  highly  rarefied  fluid,  called  the  ether, 
is  supposed  to  fill  all  space  and  to  permeate  all  bodies.     It 
fills  alike  the  spaces  among  the  planets  and  stars  and  those 
among  molecules   and   atoms.     It  is  without  weight,  and 
offers  no  resistance  to  bodies,  molecules,  or  atoms  moving 
about  in  it. 

4.  The  Structure  of  Bodies  analogous  to  that  of  the  Sidereal 
Universe.  —  The  Sidereal  Universe  is  composed  of  stars,  each 
of  which  is  probably,  like  our  own  sun,  the  centre  of  a  solar 
system  composed  of  sun  and  planets.     1\\t  planets  and  moons 
which  compose  a  solar  system  correspond  to  the  atoms  which 
compose  the  molecules,  and  the  solar  systems  correspond  to  the 
molecules  which  compose  the  body.     The  planets  in  the  solar 
system  are  sometimes  found  singly,  as  in  the  case  of  Venus,  and 
sometimes  in  groups,  as  in  the  case  of  Jupiter  and  his  moons. 
The  same  is  true  of  the  atoms  in  the  molecules. 

5.  All  Matter  is  Porous.  —  From  what  has  been  said,  it 
wiU  be  evident  that  all  matter  is  porous,  that  is,  it  contains 
spaces  which  are  not  occupied  with  material  particles.    When 
these  pores  are  too  small  to  be  seen  with  the  microscope, 
they  are  called  physical  pores.     In  wood  and  many  other 


NATURAL  PHILOSOPHY.  3 

substances  the  pores  are  large  enough  to  be  seen ;  they 
are  then  called  sensible  pores. 

6.  The  Three   Orders  of  Material    Units. — The    three 
orders  of  material  units  are  atoms,  molecules,  and  bodies. 

7.  Atomic,  Molecular,  and  Molar  Motion.  —  Every  par- 
ticle of  matter  in  the  universe  is  in  incessant  motion.     The 
atoms  are  all  the  time  moving  about  in  the  molecules  ; 
the   molecules,   in   bodies  ;   and   bodies,  in   space.     The 
motion  of  the  atoms  within  the  molecules  is  called  atomic 
motion  ;  that  of  the  molecules  in  bodies,  molecular  motion ; 
and  that  of  bodies  in  space,  molar  motion.     Molar  motion 
is  often   called  mechanical  motion.     Sometimes  the  term 
molecular  is  applied  to  the    motion   of    both   atoms  and 
molecules. 

8.  The  Three  Great  Forces  of  Nature.  —  There  are  three 
forces  corresponding  to  the  three  orders  of  material  units. 
These  are  affinity,  cohesion,  and  gravity. 

Affinity  is  the  force  which  binds  together  the  atoms  into 
molecules.  It  is  therefore  an  atomic  force.  It  is  the 
strongest  of  the  forces,  but  it  acts  only  through  infinites- 
imal distances. 

Cohesion  is  a  molecular  force.  It  binds  together  the 
molecules  into  bodies.  It  is  a  weaker  force  than  affinity, 
but  is  capable  of  acting  through  greater,  though  still  insen- 
sible distances. 

Gravity  is  a  molar  force.  It  binds  together  bodies.  It  is 
the  weakest  of  the  three  forces,  but  is  capable  of  acting 
through  all  known  distances. 

9.  Elasticity.  —  Elasticity  is   the   tendency  of  a  body  to 
spring  back  to  its  original  condition  when  it  has  been  dis- 
torted in  any  way. 

Any  distortion,  whether  produced  by  stretching,  by  bending, 
by  twisting,  by  compression,  or  by  rarefaction,  is  called  a  strain. 
The  force  which  produces  the  strain  is  called  a  stress.  Elas- 
ticity is  always  developed  by  some  kind  of  strain.  All  bodies 


4  ELEMENTS   OF 

are  elastic  to  some  extent,  but  usually,  when  the  distortion  pro- 
ceeds beyond  a  certain  point,  the  elasticity  of  the  body  breaks 
down.  This  point  is  called  the  limit  of  the  elasticity  of  the 
body. 

10.  Chemical  Properties  of  Matter.  — The  properties  of 
matter   which  grow   out    of   the    atomic  structure  of   the 
molecules  and  the  action  of   affinity  are   called  chemical 
properties. 

11.  Physical  Properties  of  Matter.  —  The  properties  of 
matter   which    grow    out    of    the   molecular   structure    of 
bodies    and    the   action    of    cohesion    are    called  physical 
properties. 

12.  The  Physical  Sciences. — The  physical  sciences  deal 
with  the  action  of  forces  on  material  units,  irrespective  of 
the  phenomena  of  life. 

Mechanics  deals  with  the  action  of  forces  and  the  laws  of 
motion,  irrespective  of  any  order  of  material  units. 

Astronomy  deals  with  gravity  and  molar  units. 

Physics  deals  with  cohesion,  molecules,  and  physical 
properties  of  matter. 

Chemistry  deals  with  affinity,  atoms,  and  chemical  prop- 
erties of  matter. 

Natural  Philosophy  includes  both  Mechanics  and  Phys- 
ics. 


NATURAL   PHILOSOPHY. 


II. 

MECHANICS. 

A.  DEFINITIONS. —  UNITS.  —  NEWTON'S  LAWS  OF  MOTION. 

13.  The  Three  Fundamental  Units. —  The  three  funda- 
mental units  of  Mechanics,  from  which  all  the  other  me- 
chanical  and   physical  units  are  derived,  are  the  unit  of 
time,  the  unit  of  length,  and  the  unit  of  mass. 

In  the  English  system  these  units  are  the  second,  the 
foot,  and  the  pound  (avoirdupois).  In  the  French  system 
they  are  the  second,  the  centimetre,  and  the  gramme. 

14.  English  and  French   Units  of  Length.  —  The  English 
standard  unit  of  length  is  the  yard,  which  is  divided  into 
three  equal  parts,  called  feet.     The  foot  is  subdivided  into 
twelve  equal  parts,  called  inches.     The  yard  is  simply  the 
length  marked  on  a  certain  rod  preserved  by  the  govern- 
ment. 

The  French  standard  unit  of  length  is  the  metre.  This 
is,  theoretically,  the  ten-millionth  of  the  distance  from  the 
equator  to  the  pole,  or  the  forty-millionth  of  the  distance 
round  the  earth.  Practically,  it  is  the  length  of  a  rod 
preserved  by  the  French  government,  which  differs  appre- 
ciably from  the  theoretical  length  of  the  metre.  The  metre 
is  about  3^  feet.  It  is  divided  into  ten,  one  hundred,  and 
one  thousand  equal  parts,  called  decimetres,  centimetres,  and 
millimetres.  Decametre,  hectometre,  and  kilometre  are,  re- 
spectively, ten  metres,  one  hundred  metres,  and  one  thou- 
sand metres.  In  the  French  or  Metric  system  of  units  the 
prefixes  deci,  centi,  and  milli  always  indicate  tenths,  hun- 


6  ELEMENTS    OF 

dredths,  and  thousandths  of  the  unit,  while  the  prefixes 
deca,  hecto,  and  kilo  always  indicate  tens,  hundreds,  and 
thousands  of  the  units. 

For  readily  comparing  the  French  units  of  length  with  our 
familiar  English  units,  it  will  be  convenient  to  remember  that  a 
metre  is  about  forty  inches  ;  a  decimetre,  about  four  inches  ; 
a  centimetre  about  T4ff  of  an  inch  ;  and  a  millimetre,  about  -fa  of 
an  inch.  A  kilometre  is  about  five  furlongs,  or  |  of  a  mile. 

15.  Units  of  Surface  and  of  Volume.  —  The  units  of  sur- 
face are  squares,  one  of  whose  sides  is  the  unit  of  length. 
Thus,  the  English  units  of  surface  are  the  square  yard,  the 
square  foot,   and  the  square   inch.     The   French    units  of 
surface  are  the  square  metre,  the  square  decimetre,  and  the 
square  centimetre. 

The  units  of  volume  are  cubes,  one  of  whose  edges  is  the 
unit  of  length.  The  English  units  of  volume  are  the  cubic 
yard,  the  cubic  foot,  and  the  cubic  inch.  The  French  units 
of  volume  are  the  cubic  metre,  the  cubic  decimetre,  and  the 
cubic  centimetre.  The  French  unit  of  capacity  is  the  cubic 
decimetre.  It  is  called  the  litre,  and  is  equal  to  about  if 
pints,  or  a  little  less  than  a  quart. 

1 6.  Units  of  Mass.  —  The  mass  of  a  body  is  the  quantity 
of  matter  wrhich  it  contains.     The  English  unit  of   mass  is 
the  mass  of  a  certain  piece  of  metal  preserved  by  the  gov- 
ernment and  called  the  pound  avoirdupois.     It  is  divided 
into  7000  equal  parts,  called  grains.     The  French  unit  of 
mass    is  the   mass  of  a  cubic  centimetre  of  water  at  its 
maximum  density.     It  is  called  a  gramme,  and  is  equal  to 
about  15^  grains.     A  kilogramme  is  equal    to  about  2\ 
pounds. 

17.  Unit  of  Density.  —  The  density  of   a  body  is    the 
quantity  of  matter  in  a  unit  of  its  volume.     The  density  of 
water  at  a  temperature  of  39°  F.  is  usually  taken  as  the 
unit  of  density. 

18.  Units  of  Velocity.  —  Velocity  is  rate  of  motion.    The 


NATURAL    PHILOSOPHY.  7 

English  unit  of  velocity  is  the  velocity  of  one/00/  a  second. 
The  French  unit  is  the  velocity  of  a  centimetre  a  second. 

When  we  speak  of  the  velocity  of  a  body  as  being  five,  ten, 
or  twenty  feet  a  second,  we  mean  that,  at  the  instant  to  which 
we  refer,  the  body  is  moving  fast  enough  to  go  five,  ten,  or 
twenty  feet  in  a  second,  provided  it  were  to  keep  on  moving  at 
the  same  rate.  It  does  not,  however,  follow  that  it  will  actually 
go  five,  ten,  or  twenty  feet  in  a  second,  for  its  rate  may  change. 

19.  The  Action  of  Forces  on  Matter.  —  Any  push  or  pull, 
of  whatever  origin,  upon  any  portion  of  matter  is  called  a 
force.     In    the  realm   of   matter   these    forces   always    act 
between  two  different  portions  of  matter.     Thus,  affinity  is 
a  pull  between  two 'atoms;   cohesion,  a  pull  between  two 
molecules;  and  gravity,  a  pull  between  two  bodies. 

The  action  of  a  pulling,  or  attractive,  force  may  be  illustrated 
by  fastening  two  balls  to  the  ends  of  an  india-rubber  cord  and 
then  separating  the  balls  so  as  to  stretch  the  cord.  The 
stretched  cord  will  pull  upon  both  balls.  The  action  of  a  push- 
ing, or  repulsive,  force  may  be  illustrated  by  placing  a  rod  of 
india-rubber  between  two  balls  and  then  crowding  the  balls 
together.  The  compressed  rubber  will  push  upon  both  balls. 

This  action  of  a  force  between  two  portions  of  matter  takes 
different  names  according  to  the  aspect  under  which  it  is  viewed. 
When  we  take  into  account  the  whole  phenomenon  of  the 
action,  we  call  it  a  stress.  This  stress,  according  to  the  mode 
in  which  it  acts,  may  be  described  as  attraction,  repulsion,  ten- 
sion, pressure,  torsion,  etc.  When  we  confine  our  attention  to 
one  of  the  portions  of  matter,  we  see  only  one  aspect  of  the 
stress,  namely,  that  which  affects  the  portion  of  matter  under 
consideration.  This  aspect  of  the  phenomenon  we  call,  with 
reference  to  its  effect,  an  external  force,  acting  upon  that  portion 
of  matter,  and,  with  reference  to  its  cause,  the  action  of  the 
other  portion  of  matter.  The  opposite  aspect  of  the  stress  is 
called  the  reaction  on  the  other  portion  of  matter. 

20.  Newton's  First  Law  of  Motion.  —  Every  body  perse- 
veres in  its  state  of  rest  or  of  moving  uniformly  in  a  straight 
line,  unless  compelled  to  change  this  stale  by  external  forces. 


8  ELEMENTS    OF 

This  is  Newton's  first  law  of  motion.  No  portion  of  matter 
in  the  universe,  so  far  as  known,  is  absolutely  at  rest. 
Were  there  such  a  portion  of  matter,  it  could  be  put  in 
motion  only  by  an  external  force. 

Bodies  are  commonly  spoken  of  as  at  rest  when  they  are  not 
changing  their  positions  with  respect  to  other  bodies  around 
them.  Thus,  we  say  that  a  body  is  at  rest  on  the  deck  of  a 
steamer,  though  it  is  really  moving  forward  with  the  steamer  ; 
and  that  bodies  are  at  rest  on  the  surface  of  the  earth,  though 
they  are  moving  along  with  the  earth.  In  all  such  cases  bodies 
are  oifly  relatively  at  rest.  In  common  language  bodies  are 
said  to  be  at  rest  with  respect  to  each  other  when  they  are  all 
moving  along  at  the  same  rate  and  in  the  same  direction. 
When,  in  common  language,  a  body  is  said  to  be  put  in  motion, 
what  really  takes  place  is  that  its  motion  is  changed  either  in 
rate  or  direction. 

Unless  acted  upon  by  external  forces,  a  moving  body 
would  always  go  on  in  a  straight  line  and  at  a  uniform  rate. 
This  seems  to  be  contradicted  by  common  experience.  All 
moving  bodies  at  the  surface  of  the  earth  show  a  decided 
tendency  to  stop.  But  all  such  moving  bodies  are  acted 
upon  by  some  external  force  acting  as  a  resistance.  The 
chief  resistances  encountered  by  moving  bodies  2ccz  friction 
and  resistance  of  the  atmosphere. 

In  proportion  as  these  resistances  are  diminished,  the  longer 
is  the  time  a  body  will  continue  to  move.  A  smooth  stone  is 
soon  brought  to  rest  when  sliding  over  the  surface  of  the  earth. 
The  same  stone  will  slide  much  longer  over  ice,  where  there  is 
less  friction.  A  top  that  will  spin  for  ten  minutes  in  the  air 
will  spin  more  than  half  an  hour  in  a  vacuum.  Since  the  time 
a  body  will  continue  in  motion  increases  in  proportion  as  the 
resistance  is  diminished,  we  may  reasonably  infer  that,  were 
the  resistance  entirely  removed,  the  body  would  continue  in  mo- 
tion forever. 

21.  Inertia.  — The  tendency  of  a  body  to  persevere  in  its 
state  of  rest  or  motion  is  called  inertia.  The  inertia  of  a 


NATURAL   PHILOSOPHY. 


body  is  directly  proportional  to  its  mass.  This  inertia  must 
be  overcome  by  some  external  force  in  order  to  put  a  body 
in  motion,  or  to  change  the  rate  or  direction  of  its  motion. 
It  takes  time  for  a  force  to  overcome  the  inertia  of  matter. 
Hence,  when  a  body  receives  a  sudden  blow,  the  part  of 
the  body  immediately  receiving  the  blow  yields  before  there 
is  time  to  overcome  the  inertia  of  the  surrounding  parts. 

There  are  many  striking  illustrations  of  inertia.  If  a  number 
of  checkers  are  piled  up  in  a  column,  one  of  them  may  be 
knocked  out  by  a  very  rapid  blow  with  a  table  knife  without 
overturning  the  column.  A  feeble  blow  will  fail.  Stick  two 
needles  into  the  ends  of  a  broomstick  and  rest  the  needles  on 

Fig.  i. 


two  glass  goblets,  as  shown  in  Figure  I.  Strike  the  middle  of 
the  stick  a  quick,  sharp  blow  with  a  heavy  poker.  The  stick 
will  break  without  breaking  the  needles  or  the  goblets.  Here 
again  a  feeble  or  indecisive  blow  will  fail.  A  soft  body,  fired 
fast  enough,  will  hit  as  hard  as  lead.  A  tallow  candle  may  be 
fired  from  a  gun  through  a  pine  board. 

22.  Centrifugal  Forfe.  —  The  so-called  centrifugal  force 
is  an  illustration  of  Newton's  first  law  of  motion.  It  is 
simply  the  tendency  of  the  parts  of  a  rotating  body  to  keep 
moving  in  straight  lines.  This  tendency  increases  with  the 
speed  of  rotation,  and  sometimes  to  such  a  degree  as  to 
overcome  the  cohesion  of  the  body.  In  this  case  the  body 
will  fly  in  pieces,  as  large  grindstones  and  heavy  fly-wheels 
have  been  known  to  do.  If  a  stone  is  fastened  to  the  end 


IO  ELEMENTS   OF 

of  a  string  and  twirled  rapidly  around  the  ringer,  the  ten- 
dency of  the  stone  to  fly  off  in  a  straight  line  may  become 
sufficient  to  break  the  string.  Iti  this  case  the  stone  will 
start  off  in  a  line  tangent  to  the  circle  it  was  describing. 

This  tendency  to  move  on  in  a  straight  line  must  be 
counteracted  by  the  force  acting  towards  the  centre,  in 
order  to  keep  a  body  moving  in  a  circle.  The  faster  the 
body  moves,  the  greater  the  pull  needed  to  keep  the  body 

Fig.  2. 


in  its  circular  path.  The  greater  the  pull  upon  the  body 
towards  the  centre,  the  greater  the  pull  of  the  body  away 
from  the  centre.  The  pull  upon  the  body  towards  the  cen- 
tre is  called  the  centripetal  force,  and  the  pull  of  the  body 
aw  ay  from  the  centre  is  called  the  centrifugal  force. 

These  two  forces  are  only  the  two  aspects  of  the  stress  of 
attraction  between  the  body  and  the  centre  about  which  it  is 
revolving. 

The  pull  of  a  revolving  body  away  from  the  centre  may  be 
illustrated  by  the  pieces  of  apparatus  shown  in  Figures  2  and 
3-  In  the  first,  two  balls  M  and  M'  are  placed  on  the  rod 


NATURAL    PHILOSOPHY. 


I  I 


Fig.*. 


A  B,  which  passes  through  them.    The  rod  is  then  put  in  rapid 
rotation  by  turning  the  crank,  and  the  balls  fly  apart. 

If  the  flexible  rings  of  Figure  3 
are  whirled  in  place  of  the  rod,  they 
will  become  more  and  more  flattened 
as  the  speed  of  rotation  increases. 
This  change  of  form  is  due  to  the 
pull  of  each  part  of  the  rings  away 
from  the  central  axis.  The  pull  will 
be  greatest  at  the  central  point  of  the 
rings,  because  this  part  is  moving 
fastest.  It  was  in  this  way  that  the 
earth  became  flattened  at  the  poles 
while  in  the  fluid  state. 

The  centrifugal  railway  (Figure 
4)  shows  a  curious  effect  of  this 
outward  pull.  A  carriage  starting 
from  A  descends  the  incline  to  B, 
passes  up  around  the  circle  C,  and 
then  up  the  incline  to  D.  The  outward  pull  of  the  carriage 
due  to  its  velocity  is  sufficient  to  keep  it  against  the  rails  while 
passing  around  the  circle,  though  it  is  part  of  the  time  travelling 
bottom  up. 

Fig.  4. 


23.  Stability  of  a  Rotating  Body. — The  tendency  of  the 
particles  of  matter  to  keep  moving  in  the  same  plane  explains 
why  a  top  will  stand  upright  so  long  as  it  is  spinning  rapidly, 
though  it  topples  over  at  once  as  soon  as  it  comes  to  rest.     For 
the  same  reason  a  bicycle  is  not  easily  overturned  while  its  large 
wheel  is  in  rapid  rotation. 

24.  External  Forces  tend  to  put  Bodies  in  Motion  or  to 


12  ELEMENTS    OF 

change  their  Velocities.  —  Suppose  a  rubber  cord  fastened  at 
one  end  to  a  body,  not  acted  on  by  any  other  force  than 
the  tension  of  the  cord,  and  suppose  the  cord  to  be  kept 
stretched  to  the  same  extent  all  of  the  time,  so  as  to  exert 
a  uniform  pull  upon  the  body.  The  body  will  begin  to 
move  in  the  direction  of  the  pull,  and  will  move  faster 
and  faster  the  longer  the  pull  continues,  gaining  the  same 
amount  of  velocity  each  second.  If  it  were  moving  at  the 
rate  of  two  feet  a  second  at  the  end  of  the  first  second,  it 
will  be  moving  at  the  rate  of  four  feet  a  second  at  the  end 
of  the  second  second,  at  the  rate  of  six  feet  a  second  at  the 
end  of  the  third  second,  and  so  on. 

25.  Units  of  Force.  —  Forces  may  be  measured  either 
by  the  pressure  which  they  would  produce  or  by  the  rate 
at  which  they  would  increase  the  velocity  of  a  mass  of 
matter. 

In  the  former  case  the  unit  of  force  is  the  force  of 
gravity  on  a  unit  of  mass.  In  the  English  system  it  is  the 
force  of  gravity  on  the  mass  of  a  pound  or  a  grain,  and  is 
called  a.  pound  or  a  grain.  In  the  French  system  it  is  the 
force  of  gravity  on  a  mass  of  a  gramme,  and  is  called  a 
gramme.  These  units  are  called  gravitation  units  ;  and 
since  they  depend  upon  the  intensity  of  gravity,  they  are 
variable,  changing  with  the  intensity  of  gravity  at  different 
places  on  the  surface  of  the  earth,  and  at  different  eleva- 
tions above  the  surface. 

In  the  latter  case  the  unit  of  force  is  the  force  that  will 
impart  to  a  unit  of  mass  a  unit  of  velocity  in  a  unit  of  time. 
In  the  English  system  it  is  the  force  that  will  impart  to  a 
mass  of  a  pound  a  velocity  of  a  foot  in  a  second.  It  is 
called  & poundal.  At  Greenwich  it  takes  32.2  poundals  of 
force  to  hold  up  a  pound. 

A  system  of  absolute  measurement  has  been  devised  in 
England,  and  adopted  by  the  British  Association.  The  units 
pf  this  system  are  all  based  upon  the  centimetre,  gramme,  and 


NATURAL    PHILOSOPHY.  13 

second  as  the  three  fundamental  units  of  length,  mass,  and 
time.  This  system  of  measurement  is  called  the  centimetre- 
gramme-second  system,  or  more  briefly,  the  C.  G.  S.  system.  Its 
units  are  called  the  centimetre-gramme-second  units,  or  more 
briefly,  the  C.  G.  S.  units. 

In  the  C.  G.  S.  system  the  unit  of  force  is  the  force  that  will 
impart  to  a  mass  of  a  gramme  a  velocity  of  one  centimetre  a 
second.  It  is  called  a  dyne.  It  takes  445,000  dynes  of  force 
to  hold  up  a  pound  at  Greenwich.  These  units  are  indepen- 
dent of  gravity,  and  are  invariable.  They  are  called  absolute 
units. 

26.  The  Impulse  of  Force.  —  The  effect  of   a   force   in 
producing  motion  is  directly  proportional  to  its  intensity  and 
the  time  during  which  it  acts.    The  product  of  the  intensity 
and  the  time  during  which  it  acts  is  called  the  impulse  of 
the  force. 

27.  Momentum.  —  The  motion  of  a  body  is  measured  by 
the  mass  and  the  velocity  of  the  body,  and  is  directly  propor- 
tional to  the  two.     If  two  bodies  have  equal  velocities,  but 
one  has  five  times  the  mass  of  the  other,  it  is  said  to  have 
five  times  the  motion  ;  or  if  the  two  have   equal  masses, 
and  one  has  five  times  the  velocity  of  the  other,  it  is  said 
to  have  five  times  the  motion  of  the  other.     The,  product 
of  the  mass  of  a  body  and  its  velocity  is  called  the  momentum 
of  the  body. 

28.  Newton's  Second  Law  of  Motion.  —  Change  of  motion 
is  proportional  to  the  impressed  force,  and  takes  place  in  the 
direction  in  which  the  force  acts.     This  is  Newton's   second 
law  of  motion. 

By  motion,  as  here  used,  Newton  means  what  is  now  called 
momentum,  in  which  the  quantity  of  matter  moved  is  taken 
into  account  as  well  as  the  rate  at  which  it  travels.  For  in- 
stance, there  would  be  the  same  change  of  motion,  whether  the 
velocity  of  four  pounds  was  changed  one  foot  a  second,  or 
the  velocity  of  one  pound  four  feet  a  second-  Jn  either  case 
the  change  of  momentum  would  be  four. 


14  ELEMENTS    OF 

By  impressed  force  Newton  means  what  is  now  called  im- 
pulse, in  which  the  time  the  force  acts  is  taken  into  account  as 
well  as  the  intensity  of  the  force.  Thus,  the  impulse,  or  im- 
pressed force,  would  be  the  same  whether  a  force  of  a  poundal 
were  acting  five  seconds  or  a  force  of  five  poundals  were  acting 
one  second.  In  either  case  the  impulse,  or  impressed  force, 
would  be  five. 

Newton's  second  law,  stated  in  terms  of  momentum,  would 
be  :  The  change  of  momentum  of  a  body  is  numerically  equal  to 
the  impulse  which  proditced  it,  and  is  in  the  same  direction. 

An  unbalanced  external  force  acting  upon  a  body  always 
changes  the  velocity  of  the  body  in  the  direction  in  which  it 
acts.  This  change  of  velocity  is  called  acceleration.  The 
acceleration  produced  in  a  given  time  by  a  force  acting 
upon  a  body  is  precisely  the  same  whether  the  body  is  at 
first  at  rest  or  in  motion,  or  whether  the  force  is  acting 
alone  or  with  other  forces. 

When  the  acceleration  is  opposed  to  the  original  motion  of  a 
body,  it  is  usually  called  a  retardation. 

Newton's  second  law,  stated  in  terms  of  acceleration,  would 
be :  When  any  number  of  forces  act  upon  a  body,  the  accelera- 
tion due  to  each  force  is  the  same  in  magnitude  and  direction  as 
if  the  others  had  not  been  in  action. 

The  total  acceleration  produced  by  the  action  of  a  force  is 
directly  proportional  to  the  impulse  of  the  force,  and  inversely 
proportional  to  the  mass  acted  upon.  A  force  of  40  poundals 
acting  for  20  seconds  upon  a  mass  of  50  pounds  would  produce 
an  acceleration  of  40  X  20  -f-  50  =  16  feet.  A  force  of  300  dynes 
acting  80  seconds  upon  200  grammes  would  produce  an  accel- 
eration of  300  X  80  -r-  200  :=  1 2o  centimetres. 

The  total  change  of  momentum  produced  by  the  action  of  a 
force  is  numerically  equal  to  the  impulse  of  the  force.  A  force 
of  40  poundals  acting  30  seconds  would  produce  a  change  of 
momentum  equal  to  40  X  30=  1200  units  (English).  A  force 
of  250  dynes  acting  20  seconds  would  produce  a  change  of  mo- 
mentum equal  to  250  X  20  =  5000  units  (C.  G.  S.)- 


NATURAL    PHILOSOPHY.  15 

QUESTIONS   ON  NEWTON'S  SECOND  LAW. 

1.  What  acceleration  would  be  produced  by  a  force  of  30 
poundals  acting  on  a  mass  of  80  pounds  for  70  seconds  ? 

2.  What  acceleration  would  be  produced  by  a  force  of  240 
dynes  acting  on  amass  of  3  kilogrammes  for  3  minutes  ? 

3.  What  must  be  the  intensity  of  a  force  that  would  give  90 
pounds  an  acceleration  of  1000  feet  in  20  seconds  ? 

4.  What  must  be  the  intensity  of  a  force  that  would  give  a 
mass  of  80  grammes  an  acceleration  of  50  metres  in  2  minutes  ? 

5.  What  must  be  the  mass  of  a  body  to  which  a  force  of  60 
poundals  would  give  an  acceleration  of  500  feet  in  30  seconds  ? 

6.  What  must  be  the  mass  of  a  body  to  which  a  force  of  500 
dynes  would  give  an  acceleration  of  8  decimetres  in  8  seconds  ? 

7.  What  momentum  would  IDC  imparted  to  a  body  by  a  force 
of  70  poundals  in  90  seconds  ? 

8     What  momentum  would  be  imparted  to  a  body  by  a  force 
of  350  dynes  in  75  seconds  ? 

9.  What  force  would  be  needed  to  change  the  momentum  of 
a  body  300  units  (English)  in  9  seconds  ? 

10.  What  force  would  be  needed  to  change  the  momentum  of 
a  body  900  units  (C.  G.  S-)  in  60  seconds? 

11.  How  long  will  it  take  a  force  of  120  poundals  to  impart  a 
momentum  of  700  units  to  a' body  ? 

12.  How  long  would  it  take  a  force  of  600  dynes  to  impart  a 
momentum  of  19,000  units  to  a  body  ? 

13.  How  long  would  it  take  a  force  of  20  poundals,  acting  in 
the  opposite  direction  to  the  motion  of  the  body,  to  stop  a  body 
having  a  momentum  of  300  units  ? 

14.  How  long  will   it  take  a  force  of  80  dynes,  acting  in  the 
opposite  direction  to  the  motion  of  the  body,  to  stop  a  body  hav- 
ing 1000  units  of  momentum  ?  Fig.  5. 

29.  Parallelogram  of  Motion.  —  To  find  "* 
the  path  of  a  body  A  (Figure  5)  acted  on 
by  two  forces  at  the  same  time,  draw  A  B 
to  represent  the  path  the  body  would  have 
taken  had  it  been  acted  on  by  the  first 
force  alone,  and  A  C  to  represent  the  path 
it  would  have  taken  had  it  been  acted  on  c 


i6 


ELEMENTS    OF 


by  the  other  force  alone.  Through  B  draw  B  D  parallel 
to  A  C,  and  through  C  draw  CD  parallel  to  AB  so  as 
to  complete  the  parallelogram  A  B  D  C.  Draw  the  diago- 
nal AD.  This  diagonal  will  represent  the  path  taken  by 
the  body  when  acted  upon  by  both  forces  together. 

30.  Newton's  Third  Law  of  Motion.  —  Newton's    third 
law  of  motion  is  as  follows :  Reaction  is  always  equal  and 
opposite  to  action  ;  that  is  to  say,  the  actions  of  two  bodies  upon 
each  other  are  always  equal  and  in  opposite  directions. 

This  law  simply  states  the  fact  that  a  force  always  acts  upon 
two  portions  of  matter  (19),  and  that  the  stress,  whether  that  of 
tension  or  pressure,  is  equal  upon  both  portions.  A  stone  raised 
from  the  earth  attracts  the  earth  just  as  much  as  the  earth 
attracts  the  stone.  Gravity  really  acts  as  a  stress  of  ten- 
sion between  the  two,  and  pulls  th'em  equally  but  in  oppo- 
site directions.  When  the  stone  falls  the  earth  moves  up  to 
meet  it.  When  the  two  meet  they  have  each  the  same  momen- 
tum, but  the  earth,  owing  to  its  great  mass,  has  only  a  very  small 
velocity.  WThen  a  cannon  is  fired,  the  igniting  powder  pushes 
back  upon  the  cannon  just  as  hard  as  it  pushes  forward  on  the 
ball.  Were  the  cannon  as  free  to  move  as  the  ball,  it  would  start 
back,  or  recoil,  with  the  same  momentum  that  the  ball  starts 
forward  with,  but  of  course  with  a  less  velocity. 

31.  Collision  of  Elastic  Bodies.  —  We  have  an  illustration  of 
action  and  reaction  in  the  collision  of  elastic  bodies.     Place  two 

ivory  balls  of  exactly 


Fig.  6. 


the  same  size  at 
the  centre  of  the 
curved  railway  in 
Figure  6.  Move  one 
of  the  balls  up  to 
one  end  of  the  track, 
and  let  it  roll  back 
against  the  ball  at 
rest-  There  will  be 
a  slight  strain  of 
compression  when 


NATURAL   PHILOSOPHY.  1 7 

the  balls  strike,  and  this  will  develop  a  stress  of  elasticity  be- 
tween them  which  will  act  equally  upon  both  and  in  opposite 
directions.  This  stress  will  stop  the  first  ball  and  start  the 
second  off  with  the  velocity  the  first  had  on  striking  it. 

Place  several  ivory  balls  of  the  same  size  on  the  centre  of  the 
track,  and  allow  the  first  ball  to  roll  against  the  end  of  "the  line. 
All  the  balls  will  remain  at  rest  except  the  last,  which  will  be 
shot  up  the  track.  In  this  case  the  strain  of  compression  and 
stress  of  elasticity  have  been  propagated  along  the  line  from 
ball  to  ball.  Each  ball  has  been  compressed  a  little  in  turn, 
and  in  recovering  itself  has  pushed  upon  the  ball  behind  it 
enough  to  stop  it,  and  upon  the  one  in  front  enough  to  flatten  it 
a  little.  Each  ball  except  the  last  was  kept  from  moving  forward 
by  the  reaction  of  the  ball  in  front. 

B.   WORK  AND  ENERGY. 

32.  Work. —  Work  is  said  to  be  done  when  anything  is 
moved  against  resistance.  We  may  consider  work  either 
with  reference  to  the  force  that  moves  the  body,  or  with 
reference  to  the  resistance  overcome.  When  we  think  of 
the  force  as  moving  the  body,  we  say  that  work  is  done  by 
the  force  upon  the  body.  When  we  think  of  the  resistance 
as  overcome  by  the  body,  we  say  that  work  is  done  by  the 
body  upon  the  resistance.  When  we  think  of  the  resist- 
ance as  impeding  the  motion  of  the  body,  we  say  that  work 
is  done  by  the  resistance  upon  the  body. 

These  terms  apply  to  different  aspects  of  the  same  work. 
Thus,  when  we  raise  a  weight,  in  winding  up  a  clock,  we  may 
say  that  work  is  done  by  the  force  used  upon  the  weight,  or 
by  the  weight  upon  or  against  gravity,  or  by  gravity  upon  the 
weight.  The  amount  of  work  done  is  the  same  in  whatever 
aspect  we  view  it.  When  the  clock  weight  runs  down  again,  we 
may  say  that  work  is  done  by  gravity  upon  the  weight,  or 
by  the  weight  upon  the  resistance  of  the  wheels,  or  by  the 
resistance  of  the  wheels  upon  the  weight,  according  to  the  aspect 
in  which  we  view  the  work.  When  a  weight  is  allowed  to  fall 
freely  to  the  earth,  the  work  done  is  that  of  increasing  the 


l8  ELEMENTS    OF 

velocity  of  the  body.     In  this  case  work  is  done  by  gravity  upon 
the  body,  and  by  the  body  upon  its  inertia. 

Work  is  done  in  every  case  in  which  the  velocity  of  a  body 
is  changed,  for  the  inertia  of  the  body  always  resists  this 
change.  . 

33.  Units  of  Work.  —  The  unit  of  work  is  the  work  done 
in  moving  anything  a  unit  of  distance  against  a  unit  of  re- 
sistance, or  by  a  unit  of  force  acting  through  a  unit  of  distance. 
A  resistance  is,  of  course,  merely  the  opposing  action  of 
some  force,  and  is  measured  in  poundals  or  dynes.     The 
English  unit  of  work  is  the  work  done  in  moving  a  mass 
against  a  poundal  of  resistance,  or  by  the  force  of  a  poundal 
acting  one  foot.     It  is  called  &foot-poundal.     The  C.  G.  S. 
unit  of  work  is  the  work  done  in  moving  a  mass  one  centimetre 
against  a  dyne  of  resistance,  or  by  the  force  of  a  dyne  acting 
one  centimetre.     It  is  called  an  erg.     There  are  421,393.8 
ergs  in  a  foot-poundal.     These  are  absolute  units. 

The  gravitation  unit  of  work  is  the  work  done  in  raising 
a  unit  of  mass  a  unit  in  height.  The  English  gravitation 
unit  is  the  work  done  in  raising  a  pound  one  foot  high.  It 
is  called  a  foot-pound.  It  varies  with  the  force  of  gravity  in 
different  parts  of  the  earth  and  at  different  elevations. 
At  Greenwich  there  are  32.2  foot-poundals  in  a  foot- 
pound. 

34.  Energy.  —  Energy  is  the  capacity  for  doing  work.     It 
is  measured  in  the   same  units  as  work,  a  unit  of  energy 
being  the  capacity  for  doing  a  unit  of  work.     Thus,  we  may 
speak  of  so  many  foot-poundals,  or  of  so  many  ergs,  of 
energy. 

The  force  that  tends  to  stop  a  moving  body  acts  upon 
it  as  a  resistance,  and  every  moving  body  has  the  power  to 
overcome  this  resistance  through  a  greater  or  less  distance 
according  to  its  momentum  and  velocity.  Hence  every 
moving  body  has  a  capacity  for  doing  work,  or  energy.  A 
body  which  is  not  in  motion  may  have  a  capacity  for  doing 


NATURAL    PHILOSOPHY.  19 

work  growing  out  of  its  condition  with  respect  to  some 
force.  Thus,  a  raised  weight  has  the  ability  to  drive  a 
clock,  compressed  steam  the  ability  to  drive  a  locomotive, 
and  a  coiled  spring  the  ability  to  drive  a  watch. 

35.  Position  of  Advantage. —  A  body  is  said  to  have  a 
position  of  advantage  with  respect  to  a  force  when  it  is  so 
situated  that  it  is  possible  for  that  force  to  put  it  in  motion. 
A  weight  raised  from  the  earth  has  a  position  of  advantage 
with  respect  to  gravity,  since  it  is  possible  for  gravity  to 
put  it  in  motion  by  pulling  it  to  the  earth  again.     For  a 
similar  reason  molecules  when  separated  from  each  other 
have  positions  of  advantage  with  respect  to  cohesion ;  and 
atoms  when  separated  from   each  other,  with  respect  to 
affinity.     A  strained  body  has  a  position  of  advantage  with 
respect  to  elasticity. 

36.  Kinetic  Energy.  —  The  energy   of  motion   is   called 
kinetic  energy. 

The  kinetic  energy  of  a  body  is  equal  to  the  product  of  the 
momentum  of  the  body  and  %  its  velocity.  Now  we  may  regard 
this  work  either  as  work  done  by  the  force  acting  as  a  resistance 
upon  the  body  or  by  the  body  upon  the  resistance. 

37.  Potential  Energy.  —  The  energy  of  position  is  called 
potential  energy.     It  is  universally  true  that  a  body,  in  re- 
turning from  a  position  of  advantage  to  its  original  posi- 
tion, does  exactly  the  same  amount  of  work  that  was  done 
upon  it  in  putting  it  in  its  position  of  advantage.     Thus,  to 
raise  a  pound  weight  12  feet  high  requires  12  foot-pounds 
of  work.     The    same  weight,   in  falling    12   feet,  will  do 
12  foot-pounds  of  work.     If  it  takes  300  ergs  of  work  to 
coil  a  spring,  the  spring  in  uncoiling  will  do  300  ergs  of 
work.      Hence    the   potential  energy  of   a  body  is  equal 
to  the  work   required  to  put  the   body   in   its  position  oj 
advantage. 


20  ELEMENTS    OF 

QUESTIONS  ON  ENERGY. 

15.  How  many  foot-poundals  of  energy  has  a  mass  of  2500 
pounds  with  a  velocity  of  5000  feet  a  second  ? 

1 6.  How  many  ergs  of  energy  has  a  mass  of  8965  grammes 
with  a  velocity  of  8000  centimetres  a  second  ? 

17.  How  many  foot-poundals  of  energy  has  a  mass  of  3  tons 
with  a  velocity  of  500  feet  a  second  ? 

1 8.  How  many  ergs  of  energy  has  a  mass  of  9  kilogrammes 
with  a  velocity  of  8  metres  a  second  ? 

C.    COMPOSITION  AND  RESOLUTION  OF  FORCES. 

38.  Representation  of  Forces  by  Lines.  — A  force  may  be 
completely  represented  by  a  line  ;  the  length  of  the   line 
representing  the  intensity  of  the  force,  the  direction  of  the 
line  the  direction  in  which  the  force  acts,  and  one  end  of  the 
line  \hz  point  of  application  of  the  force. 

39.  Resultant  and  Component  Forces.  —  There  is  usually 
some  one  force  that  would  have  the  same  effect  upon  a 
body,   in   producing  pressure   or  motion,  as   that    of   the 
several  forces  that  may  be  acting  together  upon  it.     This 
force  is  called  the  resultant  of  these  forces,  and  they  are 
called  its  components. 

40.  Composition  and  Resolution  of  Forces.  —  The  combin- 
ing of  several  forces  into  one  resultant  is  called  the  composi- 
tion of  forces  ;  and  the  decomposition  of  one  force  into  two  or 
more  components,  the  resolution  of  forces. 

In  the  composition  and  resolution  of  forces  it  is  necessary  to 
find  the  intensity,  the  direction,  and  the  point  of  application  of 
the  resultant  or  components. 

41.  The  Parallelogram   of  Forces.  —  Of  the  great  vari- 
ety of  cases  that  may  occur  in  the  composition  of  forces, 
the  most  important  is  that  in  which  two  forces  act  upon  a 
point  in  different   directions.      For  example,  let  the  two 
forces  A  B  and  A  C  (Figure  7)  be  acting  upon  the  point 
A  in   the  directions   indicated  by  the  arrows.     Through 


NATURAL     PHILOSOPHY. 


21 


Fig.  7. 


V 


B  draw  the  line  B  D  parallel  to  A  C ;  and  through  C,  the 
line  CE  parallel  to  A  B,  so 
as  to  form  the  parallelogram 
ABRC.  The  diagonal  A  R 
of  this  parallelogram  will  be 
the  resultant  of  these  two  for- 
ces. This  method  is  called 
the  parallelogram  of  forces. 

If  a  force  A  G  (Figure  8),  having  the  intensity  of  the  result- 
ant A  R,  but  the  opposite  direction,  were  applied  to  A,  it  would 
balance  this  resultant,  and,  there-  Fig.  8. 

fore,   its    components    A  B  an.d 
AC. 

The  fact  that  the  resultant  of  a- 
forces  may  be   balanced   by   an 
equal  force  applied  to  the  same 
point  in  the  opposite  direction  en- 
ables us  to  find  the  resultant  of  forces  experimentally,  and  so  to 
verify  the  above  method.     The  apparatus  for  this  experimental 

Fig.  9. 


determination  is  shown  in  Figure  9.  A  B  D  C  is  a  parallelogram 
jointed  at  its  four  corners.  Cords  pass  from  the  corners  B  and 
Cover  the  pulleys  M  and  N.  Weights  P  and  P'  are  attached 


ELEMENTS 


to  the  ends  of  these  cords.  The  number  of  ounces  in  the 
weight  P  is  equal  to  the  number  of  inches  in  the  side  A  B j  and 
the  number  of  ounces  in  P',  to  the  number  of  inches  in  A  C. 
Hang  from  A  a  weight  P",  less  than  the  sum  of  P  and  P'. 
The  parallelogram  will  take  up  a  position  of  equilibrium  such 
that  the  cords  attached  to  B  and  C  will  be  found  to  form  pro- 
longations of  the  sides  A  B  and  A  C,  and  the  diagonal  A  D  will 
be  vertical.  The  number  of  inches  in  the  diagonal  will  be 
found  to  be  equal  to  the  number  of  ounces  in  the  weight  hung 
from  A.  The  two  forces  P  and  P'  which  are  acting  on  the 
point  A  are  represented  by  the  lines  A  B  and  A  C,  and  their 
resultant  by  the  diagonal  A  D.  This  vertical  resultant  is  bal- 
anced by  the  equal  force  P"  acting  in  the  opposite  direction. 

42.  Composition  of  Several  Forces  acting  in  Different  Direc- 
tions upon  a  Point.  —  When  more  than  two  forces,  A  B,  A  C, 
A  D,  and  A  E  (Figure  10)  are  acting  in  different  directions  upon 
a  point  A,  their  resultant  may  be  Fig  1It 

found  by  the  following  method  : — 


First  find  the  resultant  A  K*-  of  the  two  forces  A  B  and  A  C  ; 
then  the  resultant  A  R1  of  the  first  resultant  A  7?1  and  of  the 
third  force  AD;  and,  finally,  the  resultant  A  Rz  of  the  second 
resultant  A  R*  and  of  the  fourth  force  A  E.  This  last  result- 
ant will  be  the  resultant  of  all  the  forces. 

43.  Resolution  of  a  Force  into  two  Oblique  Forces.  —  To 
resolve  the  force  A  R  (Figure  11)  into  two  forces  having  the 
directions  A  B  and  A  C,  draw  R  M  parallel  to  A  C,  and  R  N 
parallel  to  A  B.  A  A" and  A  J/will  represent  the  forces  required. 

The  resolution  of  forces  may  be  illustrated  by  the  case  of  a 
vessel  sailing  in  any  other  direction  than  that  of  the  wind. 


NATURAL  PHILOSOPHY.  23 

Let  the  line  A  B  (Figure  12)  represent  the  direction  of  the  keel 
of  the  vessel ;  the  line  CD,  the  direction  of  the  face  of  the  sail ; 
and  the  line  WE,  the  direction  and  intensity  of  the  wind. 
To  find  the  intensity  of  the  force  which  would  be  effective  in 
driving  the  vessel  forward,  first  resolve  the  force  of  the  wind 
IV  E  into  two  components,  one  D  E  tangent  to  the  sail,  and  the 
other  FE  perpendicular  to  the  Fig.  12. 

sail.  This  latter  component  will 
be  the  only  part  of  the  force  of 
the  wind  that  will  have  any  effect 
upon  the  sail.  This  force  must 
again  be  resolved  into  two  com- 
ponents, one  G  E  perpendicular 
to  the  length  of  the  vessel,  and 
the  other  HE  in  the  direction 
of  the  vessel.  This  last  component  will  be  the  only  portion  of 
the  force  of  the  wind  that  will  be  effective  in  moving  the  vessel 
forward. 

D.  GRAVITY  AND  EQUILIBRIUM. 

44.  Law  of  Gravity.  —  The  law  of  gravity  was  discovered 
by  Newton.    It  is  as  follows  :  Every  portion  of  matter  attracts 
every  other  portion  of  matter  with  a  force  directly  proportional 
to  the  product  of  the  masses  acted  Fig.  13. 

upon,  and  inversely  proportional 
to  the  square  of  the  distances  be- 
tween them. 

45.  Centre  of  Gravity.  —  The 
direction  of  gravity  at  the  surface 
of  the  earth  is  that  of  a  plumb- 
line.      Gravity  acts  upon    every 
particle  of  which  a  body  is  com- 
posed,   but    the     parallel    forces 
acting  upon  the  various  particles 
may  be   resolved   into   one,  and 
the  point  of   application    of  this 
resultant   is  called   the  centre  of 


ELEMENTS    OF 


gravity  of  the  body.  Thus,  G  is  the  centre  of  gravity  in  the 
stone  in  Figure  13.  The  whole  of  the  force  of  gravity  act- 
ing upon  a  body  may  be  considered  as  applied  at  the  centre 
of  gravity.  If  a  force  equal  to  the  resultant  of  the  forces  of 
gravity  is  applied  to  the  centre  of  gravity  in  the  opposite  di- 
rection, the  body  will  balance  or  be  in  equilibrium. 

The  centre  of  gravity  may  therefore  be  defined  as  the 
point  upon  which  the  body  will  balance  in  every  position. 

When  a  body  is  homogeneous  throughout,  the  centre  of  grav- 
ity is  at  the  centre  of  figure  of  the  body.  When  the  body  is 
not  homogeneous  throughout,  the  centre  of  gravity  is  away 
from  the  centre  of  figure  towards  the  denser  side  of  the  body. 
The  centre  of  gravity  often  lies  entirely  outside  of  the  material 
of  the  body,  as  in  the  case  of  a  ring  or  a  hollow  sphere.  When 
this  is  the  case,  the  centre  of  gravity  must  be  rigidly  connected 
to  the  body  in  order  to  have  the  body  balance  on  it.  A  system 
of  bodies  may  have  a  common  centre  of  gravity  lying  outside 
of  all  the  bodies.  The  centre  of  gravity  of  two  spheres  will 
lie  somewhere  on  a  line  between  their  centres  of  gravity.  If 
the  spheres  have  the  same  mass,  this  point  will  lie  just  midway 
between  their  centres  of  gravity.  If  one  sphere  has  a  greater 
mass  than  the  other,  the  centre  of  gravity  of  the  system  will  lie 
nearer  the  centre  of  gravity  of  the  larger  sphere.  If  there  is 
sufficient  difference  between  their  masses,  their  common  centre 
of  gravity  may  lie  within  the  larger  sphere. 

46.    Experimental  Method  of  finding  the  Ce?itre  of  Grav- 


Fig.  14 


ity.  —  Since  the  result- 
ant of  the  forces  of  grav- 
ity acting  upon  a  body, 
and  the  force  which  bal- 
ances it,  must  act  along 
the  same  line  in  opposite 
directions,  the  centre  of 
gravity  of  a  body  sus- 
pended so  as  to  turn 
freely  must  be  in  a  ver- 


NATURAL    PHILOSOPHY.  2$ 

tical  line  under  the  point  of  suspension.  Hence,  if  we  sus- 
pend any  body  from  two  points  and  mark  the  vertical  lines 
from  each  point  of  suspension  (Figure  14),  the  centre  of 
gravity  must  be  where  these  verticals  cross. 

47.  Kinds  of  Equilibrium.  —  When  a  body,  on  being 
tipped  a  little,  tends  to  return  to  its  old  position,  it  is  said 
to  be  in  stable  equilibrium ;  when  it  tends  to  fall  to  a  new 
position,  in  unstable  equilibrium  ;  and  when  it  rests  equally 
well  in  every  position,  in  indifferent  equilibrium. 

When  a  body  is  in  stable  equilibrium,  its  centre  of  grav- 
ity rises  on  tipping  the  body ;  when  it  is  in  unstable  equi- 
librium, its  centre  of  gravity  falls  on  tipping  the  body ; 
and  when  it  is  in  indifferent  equilibrium,  its  centre  of  grav- 
ity neither  rises  nor  falls  on  tipping  the  body. 

Fig.   15.  Fig.  16. 


48.  Equilibrium  of  a  Body  resting  on  a  Fixed  Point  or 
Axis.  —  A  body  resting  on  a  point  or  axis  can  be  in  equi- 
librium only  when  the  centre  of  gravity  and  the  point  or 
axis  of  support  lie  in  the  same  vertical  line.  This  can  be 
the  case  only  when  the  centre  of  gravity  is  either  directly 
above  or  below  the  point  or  axis  of  support.  In  the  former 
case  the  body  is  in  unstable  equilibrium.  This  case  is 
shown  in  Figure  15.  O  is  the  axis  of  support,  and  G  the 
centre  of  gravity.  It  will  be  seen  that  gravity  will  tend  to 


26 


ELEMENTS    OF 


Fig.  17. 


topple  the  body  over  as  soon  as  it  is  tipped.  In  the  latter 
case  the  body  is  in  stable  equilibrium.  This  case  is  shown 
in  Figure  16.  As  soon  as  the  body 
is  tipped  gravity  tends  to  right  it. 

The  toy  called  the  balancer  (Figure 
17)  is  an  illustration  of  stable  equi- 
librium in  a  body  resting  on  a  point. 
The  balls  at  the  ends  of  the  wires  at 
each  side  of  the  figure  bring  the  centre 
of  gravity  of  the  whole  below  the  toe 
on  which  the  figure  is  resting. 

In  a  similar  way  a  Fig.  is. 
cork  may  be  balanced 
on  the  point  of  a  needle 
by  sticking  two  forks 
into  it,  as  shown  in 
Figure  18. 

When  the  centre  of' 
gravity  is  at  the  point 

or  axis  of  support,  the  body  is  in  indifferent 
equilibrium. 

49.  Equilibrium  of  a  Body  resting  on  a  Horizontal  Plane 
at  One  Point  only.  —  Such  a  body  can  be  in  equilibrium 
only  when  its  centre  of  gravity  and  the  point  where  it 


Fig.  19. 


touches  the  plane  are  both  in  the  same  vertical.  Figure 
19  represents  two  positions  of  equilibrium  of  an  oval  body 
on  a  horizontal  plane.  In  the  first  case  the  body  is  in 
unstable  equilibrium,  because  its  centre  of  gravity  will 


NATURAL    PHILOSOPHY. 


begin  to  fall  as  soon  as  it  is  tipped.  In  the  second  case 
the  body  is  in  stable  equilibrium,  because  its  centre  of 
gravity  is  in  its  lowest  possible  position. 

Fig.  20. 


The  toy  call 


ler  (Figure  20)  is  an  illustration  of 


stable  equilibrium  of  a  body  touching  a  horizontal  plane  at  one 
point.  The  centre  of  gravity  is  so  low  down  that  the  body  can- 
not be  tipped  without  raising  this  point. 

50.  Equilibrium  of  a  Body  resting  on  a  Horizontal  Plane 
at  Several  Points.  —  Such  a  body  will  be  in  stable  equilib- 
rium when  the  vertical  line  Fig.  21. 

from  its  centre  of  gravity 
passes  within  the  polygon 
formed  by  joining  the  several 
points  on  which  the  body  rests, 
as  in  Figure  21.  This  poly- 
gon is  called  the  base  of  the  gi 

body.    The  lower  the  centre  y 

of  gravity,  and  the  greater 

the  distance  of  its  vertical  from  the  nearest  side  of  the 
base,  the  greater  the  stability  of  the  equilibrium  of  the 
body,  because  the  farther  the  body  would  ha^e  to  be 
tipped,  and  the  more  its  centre  of  gravity  would  have  to 
be  raised,  to  overturn  it  (Figure  22). 

In  Figure  22,  in  order  to  overturn  either  of  the  bodies  abed, 
we  must  tip  it  so  as  to  carry  its  centre  of  gravity  £•  through  the 
raise  it  through  the  distance  he;  and  it  is  evident  that 
he  are  greater  in  the  case  of  the  right-hand  body. 


28 


ELEMENTS    OF 


For  this  reason  a  high  load  on  a  wagon  is  more  likely  to  tip 
over  than  a  low  one.  A  leaning  body,  like  the  famous  Leaning 
Tower  at  Pisa,  may  be  in  stable  equilibrium,  because  the  verti- 
cal from  the  centre  of  gravity  falls  within  the  base. 

Fig.  22. 


51.  Weight. —  Weight  is  the  downward  pressure  which 
gravity  causes  a  body  to  exert.  While  a  body  will  have  the 
same  mass  wherever  it  may  be,  its  weight  will  vary  with 
the  force  of  gravity  acting  upon  it.  As  this  force  is  in- 
versely proportional  to  the  square  of  the  distance  (44),  at 
twice  the  distance  from  the  centre  of  the  earth  a  body 
would  have  only  one  fourth  the  weight  it  has  at  the  sur- 
face of  the  earth.  On  the  sun,  which  has  a  much  greater 
mass  than  the  earth  (44),  the  same  body  would  have  28 
times  the  weight  it  has  on  the  earth.  The  English  unit  of 
weight  is  the  pound  avoirdupois ;  the  French  unit  is  the 
gramme. 

The  weight  of  a  body  is  ascertained  either  by  finding  how 
much  it  will  bend  a  spring,  as  in  the  spring  balance,  or  by  find- 
ing how  many  known  weights  at  one  end  of  a  beam  will  coun- 
terpoise it  when  placed  on  the  other  end,  as  in  the  ordinary 
balance.  By  the  last  method  the  weight  of  the  body  would  be 
found  to  be  the  same  everywhere,  for  it  is  not  the  weight  of  the 
body  which  is  found  in  this  case,  but  its  mass.  This  is  found 
by  comparing  the  weight  of  a  body  with  that  of  a  known  mass. 
The  weight  of  the  mass  to  be  weighed,  and  that  of  the  mass 
used  to  counterpoise  it,  both  change  with  the  force  of  gravity. 


NATURAL    PHILOSOPHY. 


29 


Fig.  23. 


52.  The  Balance.  —  The  balance  (Figure  23)  consists  of 
a  rigid  bar  A  B,  called  the  beam,  supported  on  an  axis  O 
at  its  centre.     This  axis  is 

just   above    the    centre    of 

gravity  of    the   beam,   that 

the  beam  may  be  in  stable 

equilibrium.        When      the 

beam  is  exactly  horizontal, 

it  is   in    equilibrium.     Two 

scale   pans    are    suspended 

from  the  ends  of  the  beam 

at  equal  distances  from  the 

axis.       The     body    to     be 

weighed  is  placed  in  one  pan,   and  is  counterpoised  by 

known  weights  in  the  other. 

53.  Specific  Gravity.  —  The  specific  gravity   of   a   sub- 
stance is  its  weight  compared  with  the  weight  of  the  same 
bulk  of  some  standard  substance.     The  substance  commonly 
taken  as  the  standard  for  solids  and  liquids  is  distilled 
water  at  a  temperature  of  39°  F.     A  cubic  foot  of  such 
water  weighs   62.425   Ibs.   avoirdupois.     The  weight  of  a 
gallon  of  water  is   10  Ibs.     The  weight  of  a  cubic  centi- 
metre of  water  is  a  gramme,  and  the  weight  of  a  litre  of 
water  is  a  kilogramme. 

In  the  following  table  we  give  the  specific  gravities  of  some 
liquids  and  solids. 

Liquids,  at  Temperature  of  Freezing  Water. 


Water,  sea,     ....  1.026 

Alcohol,  pure       .     .     .     .791 

"         proof  spirit      .     .916 

Ether 716 

Mercury     ....      13.596 
Naphtha 848 


Oil,  linseed 940 

"  olive 915 

"  whale 923 

"  turpentine  .  .  .  .870 
Blood,  human .  .  .  .1.055 
Milk,  of  cow  .  .  .  .1.03 


ELEMENTS    OF 


Solids. 


Copper 8.95 

Gold 19.26 

Iron 7.79 

Indium 22.4 

Lead 11.4 

Platinum       .     .     .     .     21.5 

Silver 10.5 

Tin 7.3 

Zinc 6.9 


Ice 92 

Basalt 3.00 

Clay 1.92 

Glass,  crown     ...        2.5 
"      flint     ....        3.0 
Quartz  (rock  crystal)  .        2.65 

Fir,  spruce 48  to  .7 

Oak,  European      .    .69  to  .99 
Lignum-vitae     .     .    65  to  1.33 


The  weight  of  a  cubic  foot  of  any  substance  is  equal  to 
62.425  Ibs.  avoirdupois  multiplied  by  its  specific  gravity. 

The  weight  of  a  cubic  centimetre  of  any  substance,  in 
grammes,  is  equal  to  its  specific  gravity. 

The  weight  of  a  litre  (or  cubic  decimetre)  of  any  substance, 
in  kilogrammes,  is  equal  to  its  specific  gravity. 

The  weight  of  a  gallon  of  any  liquid,  in  Ibs.  avoirdupois,  is 
equal  to  its  specific  gravity  multiplied  by  10. 

QUESTIONS  ON   THE  ABOVE    TABLE. 

19.  What  is  the  weight  of  a  cubic  foot  of  mercury  ? 

20.  What  is  the  weight  of  a  gallon  of  milk  ? 

21.  How  many  gallons  in  50  Ibs.  of  pure  alcohol  ? 

22.  What  is  the  weight  of  15  litres  of  ether  ? 

23.  How  many  litres  in  8  kilogrammes  of  olive  oil  ? 

24.  What  is  the  weight  of  a  cubic  yard  of  clay  ? 

25.  What  is  the  weight  of  a  cubic  foot  of  flint  glass  ? 

26.  What  is  the  weight  of  a  cubic  inch  of  silver? 

27.  How  many  cubic  feet  in  a  ton  of  ice  ? 

28.  How  many  cubic  inches  in  a  pound  of  quartz  ? 

29.  What  is  the  weight  of  a  cubic  decimetre  of  silver? 

30.  What  is  the  weight  of  a  cubic  metre  of  lead  ? 

E.   FALLING  BODIES. 

54.    All  Bodies  fall  at  the  Same  Rate  in  a  Vacuum.  ~ 
That  light   and   heavy  bodies   fall   at  the  same  rate  in  a 
vacuum   may  be  shown  with  the  guinea  and  feather  tube 


NATURAL    PHILOSOPHY. 


(Figure  24).  The  tube  contains  a  bit  of  metal  and  a 
feather.  Exhaust  the  air  from  the  tube,  and  invert  the 
tube.  The  metal  and  the  feather  will  Fig.  24. 

be  seen    to    fall   through    the   tube   at 
the  same  rate. 

The  reason  that  light  and  heavy  bodies 
fall  in  a  vacuum  at  the  same  rate  is  that 
the  force  of  gravity  acting  upon  a  body 
varies  directly  as  the  mass  of  the  body. 
The  force  of  gravity  on  a  mass  of  a  pound 
is  about  32  poundals  ;  on  a  mass  of  two 
pounds,  64  poundals ;  on  a  mass  of  half  a 
pound,  16  poundals ;  on  a  mass  of  one 
ounce,  2  poundals ;  etc.  The  force  of 
gravity  on  a  mass  of  one  gramme  is  about 
981  dynes;  on  a  mass  of  a  decagramme, 
9810  dynes  ;  on  a  mass  of  a  decigramme, 
98.1  dynes;  etc.  Since  the  intensity  of 
the  gravity  acting  upon  a  body  increases 
just  as  rapidly  as  the  mass  of  the  body, 
gravity,  if  left  to  itself,  would  cause  all 
bodies  to  fall  at  the  same  rate  ;  for  if  the 
mass  of  one  body  is  twice  or  thrice  as 
great  as  that  of  another,  gravity  will  act 
upon  it  with  twice  or  thrice  the  intensity. 

55.  Bodies  fall  with  Unequal  Veloci- 
ties in  the  Air.  —  A  bullet  will  fall 
through  the  air  much  faster  than  a  feather.  The  air  offers 
resistance  to  every  body  falling  through  it.  The  denser  a 
body  and  the  less  its  surface,  the  less  its  motion  is  re- 
tarded by  the  air.  Gold-leaf  falls  slowly  in  the  air,  while 
the  same  gold  in  the  form  of  a  solid  sphere  would  fall 
almost  as  rapidly  in  the  air  as  in  a  vacuum. 

The  resistance  of  the  air  increases  with  the  velocity,  and 
after  a  while  it  becomes  equal  to  the  attraction  of  gravity  upon 
a  body.  When  this  is  the  case,  the  body  will  gain  no  more 


32  ELEMENTS    OF 

velocity,  but  keep  falling  at  a  uniform  rate.  Were  a  body  shot 
downward  with  a  velocity  greater  than  this,  it  would  be  retarded 
by  the  resistance  of  the  air,  which  would  then  be  greater  than 
the  pull  of  gravity,  until  its  velocity  were  reduced  to  that  at 
which  the  resistance  of  the  air  would  be  just  equal  to  the  pull 
of  gravity. 

56.  Acceleration  produced  by  Gravity.  —  When  bodies 
are  falling  near  the  earth,  gravity  increases  their  velocity  at 
the  uniform  rate  of  about  32.2  feet  a  second,  in  a  vacuum. 
This  acceleration  per  second  produced  by  gravity  is  usually 
represented  by  £",  and  is  called  the  intensity  of  gravity.  It 
is  equal  to  about  981  centimetres,  or  9.81  metres.  When  a 
body  is  rising,  gravity  retards  its  velocity  at  the  rate  of  32.2 
feet,  or  9.81  metres  a  second.  Were  a  body  thrown  up  in 
a  vacuum,  it  would  be  just  as  many  seconds  in  falling  as  it 
is  in  rising,  and  it  would  reach  the  point  it  started  from 
with  the  velocity  it  had  on  starting.  It  gains  just  as  much 
velocity  in  falling  as  it  lost  in  rising. 

The  velocity  acquired  by  a  body  falling  from  a  state  of  rest 
will  be  equal  to  the  proditct  of  the  intensity  of  gravity  and  the 
number  of  seconds  the  body  has  been  falling.  If  we  represent 
the  velocity  acquired  by  ?/,  and  the  number  of  seconds  the  body 
has  been  falling  by  /,  the  formula  for  the  velocity  of  a  body 
falling  from  a  state  of  rest  will  be  v=.gt. 

If  a  body  were  falling  from  a  state  of  rest,  the  number  of  feet 
of  velocity  it  would  acquire  in  20  seconds  would  be  32.2  X  20 
=  644  ;  and  the  number  of  metres  of  velocity  it  would  acquire 
would  be  9.81  X  20  =  196.2. 

The  distance  passed  over  by  a  moving  body  is  always  equal 
to  the  product  of  its  mean  velocity  and  the  time.  Since  falling 
bodies  gain  velocity  at  a  uniform  rate,  the  mean  velocity  of  a 
body  falling  from  a  state  of  rest  will  be  one  half  the  velocity  it 
has  acquired.  As  the  velocity  is  =gt,  the  mean  velocity  will 
be  ]/2  gt.  If  we  represent  the  space  passed  over  by  s,  we  shall 
have 


The  distance  passed  over  by  a  body  falling  4  seconds  from 


NATURAL    PHILOSOPHY.  33 

a  state  of  rest  would  be  equal  to  i6.h  X  1  6  r=  257.6  feet,  or  to 
4.9  x  16=  78.4  metres. 
From  the  formula 


we  have 


V 

~  Z 


Substituting  this  value  of/  in  the  formula 
we  have 

"  */ 

QUESTIONS  ON  FALLING  BODIES. 

31.  How  long  would  it  take  a  body  falling  from  a  state  of  rest 
to  acquire  a  velocity  of  193.2  feet  ? 

If          I Q3- 2 

/  —  -  =  — —  ^=  6  seconds. 
g        32.2 

32.  How  long  would  it  take  a  body  falling  from  a  state  of 
rest  to  acquire  a  velocity  of  39.24  metres  a  second  ? 

v       39.24 
/  =  -  =  =~ —  =  4  seconds. 

33.  How  far  must  a  body  fall  from  a  state  of  rest  to  acquire 
a  velocity  of  1500  feet  a  second  ? 

7/2  2250000 

J  =  2^  r    "644"    =  34938  feet- 

34.  How  far  must  a  body  fall  from  a  state  of  rest  to  acquire 
a  velocity  of  800  metres  a  second  ? 

v2       640000 
s  ~  2g  =~   19.62  =  326l9-7  metres. 

35.  How  many  feet  of  velocity  would  a  body  acquire  in  falling 
25  seconds  from  a  state  of  rest  ? 

36.  How  many  metres  of  velocity  would  a  body  acquire  in 
falling  42  seconds  from  a  state  of  rest  ? 

37.  How  long  would  a  body  have  to  fall  from  a  state  of  rest 
to  acquire  a  velocity  of  986  feet  ? 

3 


34  ELEMENTS    OF 

38.  How  long  would  a  body  have  to  fall  from  a  state  of  rest 
to  acquire  a  velocity  of  25,000  centimetres  a  second  ? 

39.  How  many  feet  would  a  body  fall  from  a  state  of  rest  in 
32  seconds  ? 

40.  How  many  metres  would  a  body  fall  from  a  state  of  rest 
in  45  seconds  ? 

41.  How  far  would  a  body  have  to  fall  from  a  state  of  rest  to 
acquire  a  velocity  of  1200  feet  a  second  ? 

42.  How  far  would  a  body  have  to  fall  from  a  state  of  rest  to 
acquire  a  velocity  of  300  metres  a  second  ? 

57.  The  Height  to  which  a  Body  can  rise.  —  A  body  moving 
upward  will  continue  to  rise  till  all  of  its  velocity  is  exhausted. 
A  rising  body  loses  velocity  just  as  fast  as  a  falling  body  gains 
it.  Hence  the  height  to  which  a  body  can  rise  with  a  given 
velocity  is  just  equal  to  the  height  from  which  it  must  fall  to 
gain  that  "velocity.  The  height  to  which  a  body  can  rise  will 
therefore  be  represented  by  the  formula 


In  this  case  s  is'  the  distance  a  body  can  rise,  and  v  the 
velocity  with  which  it  starts.  The  height  to  which  a  body  can 
rise  increases  as  the  square  of  the  velocity  with  which  it  starts. 

58.  Transformation  of  Energy  in  the  Case  of  a  Body  pro- 
jected upward.  —  When  a  body  is  projected  upward,  its  energy 
on  leaving  the  surface  of  the  earth  is  entirely  kinetic.  As  it 
rises,  it  moves  slower  and  slower,  and  so  loses  kinetic  energy, 
but  as  it  is  separated  farther  and  farther  from  the  earth,  it  gains 
potential  energy.  At  the  highest  point  the  body  reaches,  its 
energy  is  entirely  potential.  As  it  falls  again,  it  moves  faster 
and  faster,  and  so  gains  kinetic  energy,  but  as  it  comes  nearer 
and  nearer  the  earth,  it  loses  potential  energy.  While  the  body 
is  rising  its  kinetic  energy  is  gradually  transformed  into  poten- 
tial energy;  and  when  it  falls  again,  its  potential  energy  is 
changed  back  again  into  kinetic  energy.  The  energy  possessed 
by  the  body  is  precisely  the  same  at  every  point  in  its  path. 
When  the  body  strikes  the  earth,  its  energy  is  apparently 
destroyed  ;  but  when  we  come  to  the  subject  of  Heat,  we  shall 
see  that  this  is  not  really  the  case. 


NATURAL    PHILOSOPHY.  35 

59.  The  Path  of  a   Body  projected  horizontally  or   ob- 
liquely. —  When    a    body    is    projected    horizontally    or 
obliquely,  gravity  draws  it  towards  the  earth   faster  and 
faster  the  longer  it  acts  upon  it,  and  so  causes  it  to  describe 
a  curved  path.     The  curve  in  this  case  would  be  a  parabola 
were  it  not  for  the  resistance  of  the  air. 

The  curved  line  in  Figure  25  shows  approximately  the  path 
of  a  cannon-ball  through  Fig.  25. 

the  air,  when  fired  in  the 
direction  of  A  B.  The 
line  A  C  represents  the 
range  of  the  ball,  or 
the  greatest  horizontal  A 
distance  it  is  thrown.  Were  it  not  for  the  resistance  of  the  air, 
the  range  would  be  greatest  when  the  cannon  was  pointed  45° 
above  the  horizon. 

60.  Intensity  of  Gravity.  —  The  intensity  of  gravity  varies 
as  we  pass  from  the  equator  to  the  poles.     At  the  equator  its 
intensity  is  sufficient  to  give  a  mass  in  a  vacuum  an  acceleration 
of  32.088  feet  per  second,  while  at  the  poles  it  is  sufficient  to 
give  a  mass  in  a  vacuum  an  acceleration  of  32.253  feet  per 
second.    The  value  of  g  in  centimetres  varies  from  978.10  at  the 
equator  to  983.11  at  the  poles.     The  intensity  of  gravity  also 
varies  u'iih  the  height  (44).     At  twice  the  distance  from  the 
centre  of  the  earth,  the  intensity  of  gravity  is  only  one  fourth  as 
great ;  at  three  times  the  distance,  one  ninth  as  great ;  and  so  on. 

Since  uponndal  is  a  force  that  will  give  to  a  mass  of  a  pound 
an  acceleration  of  a  foot  in  a  second,  and  since  gravity  will  give 
a  mass  of  a  pound  an  acceleration  of  32.2  feet  a  second,  it  follows 
that  there  are  about  32.2  poundals  in  a  pound  at  Greenwich 
as  has  already  been  stated  (33).  A  poundal  is  about  half  ar4 
ounce.  The  number  of  poundals  in  a  pound  at  any  place  is 
equal  to  the  value  of  g  in  feet  at  that  place. 

Since  gravity  will  give  a  mass  of  a  gramme  an  acceleration 
of  981  centimetres,  it  follows  that  there  are  981  dynes  in  a 
gramme  of  force  at  Greenwich.  The  number  of  dynes  in  a 
gramme  at  any  place  is  equal  to  the  value  of  g  in  centimetres  at 
that  place. 


36  ELEMENTS    OF 

The  value  of  g  at  any  place   is  ascertained  by  means  of  a 
pendulum. 

F.  THE  PENDULUM. 

6 1.  The  Pendulum.  —  Any  body  free  to  turn  on  a  hori- 
zontal axis  which  does  not  pass  through  its  centre  of 
gravity  can  be  in  stable  equilibrium  only  when  its  centre 
Fig.  26.  of  gravity  is  below  the  axis  of  support  and  in  the 
same  vertical  plane  with  it.  When  pulled  aside 
from  this  position  o'f  equilibrium  and  released,  the 
body  will  vibrate  to  and  fro  across  its  position  of 
stable  equilibrium,  until  friction  and  the  resistance 
of  the  air  bring  it  to  rest.  A  body  suspended  in 
this  way,  no  matter  what  its  shape,  is  called  a 
pendulum.  The  usual  form  of  the  pendulum  is 
that  shown  in  Figure  26.  It  consists  of  a  rod 
which  can  turn  on  an  axis  O  at  its  upper  end,  and 
which  carries  a  heavy  piece  of  metal  M,  called 
the  ball,  at  its  lower  end.  The  ball  can  be  raised 
or  lowered  by  means  of  the  screw  V. 

The  arc  described  by  the  pendulum  is  called 
the  amplitude  of  the  vibration,  and  the  time  it 
takes  to  describe  it  is  called  the  time  of  vibration. 

62.  The  Laws  of  the  Pendulum.  —  It  has  been 
found,  by  mathematical  investigation,  that  for 
small  vibrations  the  time  of  vibration  is  independent 
of  the  amplitude  ,•  also,  that  the  time  of  vibration 
increases  as  the  square  root  of  the  length  of  the  pendulum,  and 
decreases  as  the  square  root  of  the  intensity  of  gravity  increases. 
In  other  words,  when  the  amplitude  does  not  exceed  3°  or 
4°,  the  same  pendulum  will  vibrate  at  the  same  rate,  no 
matter  what  may  be  the  amplitude  of  vibration;  but  if  the 
pendulum  is  made  four,  nine,  or  sixteen  times  as  long,  it 
will  vibrate  one  half,  one  third,  or  one  fourth  as  fast ; 
while,  if  a  pendulum  were  kept  of  the  same  length,  and  the 


NATURAL    PHILOSOPHY.  37 

intensity  of  gravity  were  to  become  four,  nine,  or  sixteen 
times  as  great,  the  pendulum  would  vibrate  two,  three,  or 
four  times  as  fast. 

63.  Simple  and  Compound  Pendulums.  — The  simple  pen- 
dulum is  an  ideal  one,  whose  ball  is  a  single  heavy  particle 
suspended  by  a  line  without  weight.  Every  pendulum  actually 
used  is  a  compound  one,  consisting  of  a  heavy  weight  hung 
from  a  fixed  point  by  means  of  a  rod  of  wood  or  metal.  Each 
particle  of  such  a  pendulum  may  be  regarded  as  a  simple  pen- 
dulum ;  but  as  these  particles  are  at  different  distances  from 
the  point  of  suspension,  they  tend  to  vibrate  at  different  rates. 
The  particles  near  the  point  of  suspension  are  retarded  by  the 
tendency  of  the  particles  below  them  to  vibrate  at  a  slower  rate, 
while  the  particles  near  the  lower  end  of  the  pendulum  are 
accelerated  by  the  tendency  of  the'  particles  above  them  to 
vibrate  more  rapidly.  At  some  point  between  these  there  must 
be  a  particle  whose  vibration  is  neither  retarded  nor  accelerated. 
As  this  particle  is  vibrating  at  its  normal  rate,  its  distance  from 
the  point  of  suspension  must  be  the  length  of  a  simple  pendulum 
that  would  vibrate  at  the  rate  of  the  compound  pendulum.  The 
point  where  this  particle  is  situated  is  called  the  centre  of  vibra- 
tion •  and  its  distance  from  the  point  of  suspension,  the  virtual 
length  of  the  pendulum. 

If  a  pendulum  is  inverted  and  suspended  by  its  centre  of 
vibration,  the  former  point  of  suspension  becomes  its  new  centre 
of  vibration.  This  remarkable  property  of  a  compound  pen- 
dulum enables  us  readily  to  find  the  centre  of  vibration.  We 
have  only  to  reverse  the  pendulum,  and  find,  by  trial,  the  point 
at  which  it  must  be  suspended  to  vibrate  at  the  same  rate  as 
before.  A  pendulum  constructed  for  this  purpose  is  called  a 
reversible  pendulum. 

64.  Use  of  the  Pendulum  for  measuring  Time.  —  The 
most  important  use  of  the  pendulum  is  for  measuring  time. 
A  common  clock  is  an  instrument  for  keeping  a  pendulum  in 
vibration,  and  recording  its  beats. 

The  essential  parts  of  the  arrangement  by  which  this  is  accom- 
plished are  shown  in  Figure  27.  The  'scape-wheel  R  is  turned 


ELEMENTS    OF 


by  a  weight  or  spring,  and  its  motion  is  regulated  by  means  of 
the  escapement  m  n.     This  turns  on  the  axis  o,  and  is  connected 
Fig.  27.  with  the   pendulum  rod   by  means   of   the 

forked  arm  a  b.  When  the  pendulum  is  at 
rest,  the  hooks  n  and  in  of  the  escapement 
catch  the  teeth  of  the  scape-wheel,  and  keep 
it  from  turning.  As  the  pendulum  vibrates, 
the  hooks  of  the  escapement  alternately 
release  and  catch  the  teeth  of  the  scape- 
wheel,  and  so  compel  it  to  turn  slowly,  and 
at  a  uniform  rate.  The  hooks  of  the  es- 
capement are  of  such  shape  that  each  tooth 
of  the  scape-wheel,  as  it  slips  off  the  hook, 
gives  the  escapement  a  little  push  so  as  to 
keep  up  the  vibration  of  the  pendulum. 

Each  tooth  of  the  scape-wheel  is  caught 
twice  during  the  revolution  of  the  wheel, 
once  by  each  hook  of  the  escapement. 
Hence,  if  the  scape-wheel  has  thirty  teeth, 
it  will  make  one  revolution  for  every  sixty 
beats  of  the  pendulum.  The  axis  of  the 
scape-wheel  carries  the  second-hand  of  the 
clock,  which  registers  the  beats  of  the  pen- 
dulum up  to  sixty.  The  scape-wheel  is  con- 
nected with  another  which  turns  g1^  as  fast. 
The  axis  of  this  wheel  carries  the  minute- 
hand,  which  registers  the  revolution  of  the  second-hand  up  to 
sixty.  This  second  wheel  is  connected  with  a  third  which  turns 
i1^  as  fast  as  itself.  The  axis  of  this  last  wheel  carries  the  hour- 
hand,  which  registers  the  revolution  of  the  minute-hand  up  to 
twelve,  or  half  a  day. 

65.  Transformations  of  Energy  in  the  Vibrations  of  the 
Pendulum.  —  When  the  pendulum  reaches  its  farthest  point 
to  the  right  or  left,  its  energy  is  entirely  potential ;  and  when 
its  ball  is  at  its  lowest  point,  its  energy  is  entirely  kinetic.  As 
the  ball  rises,  its  kinetic  energy  is  transformed  into  potential 
energy,  and  as  it  falls  again,  its  potential  energy  is  transformed 
into  kinetic  energy. 

The  energy  consumed  in  overcoming  the  friction  of  the  axis 


NATURAL    PHILOSOPHY.  39 

of  the  pendulum  and  of  the  wheels  of  the  clock  and  the  resist- 
ance of  the  air  is  supplied  by  the  falling  weight  or  uncoiling 
spring  ;  and  when  the  store  of  energy  in  the  weight  or  spring  is 
consumed,  it  must  be  renewed  by  again  raising  the  weight  or 
coiling  the  spring  in  winding  up  the  clock.  This  new  supply  of 
energy  is  drawn  from  the  hand  and  arm  of  the  person  who  winds 
the  clock. 

G.  MACHINES. 

66.  Simple  Machines.  —  A  machine  is  an  instrument  by 
which  a  force  is  applied  to  do  work.     Every  machine,  how- 
ever complicated,  is  made  up  of  a  very  few  elements,  called 
simple  machines,  or  mechanical  powers.    These  are  the  lever, 
the  wheel  and  axle,  the  pulley,  the  inclined  plane,  the  wedge, 
and  the  screw. 

The  force  applied  to  work  the  machine  is  called  the 
power ;  and  the  resistance  overcome  by  the  machine,  the 
work. 

A  perfect  machine  would  be  one  which  offered  no  friction  or 
other  resistance  of  its  own.  Such  a  machine  has  only  an  ideal 
existence.  In  every  machine  in  actual  use  the  work  done  is 
partly  useful  in  overcoming  the  resistance  we  desire  to  over- 
come, and  partly  useless  in  overcoming  the  resistance  of  the 
machine  itself.  In  the  theory  of  machines  the  resistance  of  the 
machine  itself  is  left  out  of  view.  The  magnitude  of  the  resist- 
ance to  be  overcome  is  represented  by  a  rising  weight,  and  the 
magnitude  of  the  power  is  usually  represented  by  a  falling 
weight.  The  resistance  is  often  called  the  weight. 

67.  The  General  Law  of  Machines.  —  The  work  done  by 
the  power  upon  a  machine,  and  the  work  done  by  a  machine 
upon  the  resistance,  are  simply  different  aspects  of  the  same 
work  (32),  and  hence  they  are  equal  in  amount.    Now  the 
work  done  by  a  falling  weight  is  equal  to  the  product  of  the 
weight  and  the  distance  it  falls,  and  the  work  done  in  raising 
a  weight  is  the  product  of  the  weight  and  the  distance  it  is 
raised.    If,  then,  we  represent  the  work  done  by  the  power 
upon  the  machine  by  a  falling  weight,  and  the  work  done 


40  ELEMENTS    OF 

by  the  machine  upon  the  resistance  by  a  rising  weight,  we 
arrive  at  the  following  general  law  of  machines  :  The  power 
multiplied  by  the  distance  through  which  it  moves  is  always 
equal  to  the  weight  multiplied  by  the  distance  through  which  it 
moves.  This  law  is  often  stated  thus  :  In  any  machine,  the 
power  and  weight  will  be  in  equilibrium  when  they  are  in  the 
inverse  ratio  of  their  velocities. 

The  following  facts  result  from  the  general  law  of  machines 
just  stated  :  — 

(i.)  The  faster  the  power  moves,  compared  with  the  weight, 
the  greater  the  weight  it  will  balance. 

(2.)  When  the  power  moves  faster  than  the  weight,  it  will 
balance  a  weight  greater  than  itself ;  and  when  it  moves  slower 
than  the  weight,  it  will  balance  a  weight  less  than  itself  ;  and 
when  it  moves  just  as  fast  as  the  weight,  it  will  balance  a  weight 
equal  to  itself. 

(3.)  The  power  will  balance  a  weight  just  as  many  times  itself 
as  its  velocity  is  times  that  of  the  weight. 

68.  Gain  and  Loss  of  Power  in  a  Machine.  —  When,  in 
any  machine,  the  power  balances  a  weight  greater  than 
itself,  there  is  said  to  be  a  gain  of  power,  or  mechanical 
advantage ;  and  when  the  power  balances  a  weight  less 
than  itself,  a  loss  of  power,  or  mechanical  disadvantage. 

When  there  is  a  gain  of  power  there  is  always  a  corre- 
sponding loss  of  speed,  and  when  there  is  a  loss  of  power 
there  is  a  corresponding  gain  of  speed. 

A  machine  might  be  described  as  an  instrument  by  which  we 
change  the  point  at  which  the  power  acts,  the  direction  in  which 
it  acts,  or  the  rate  at  which  it  acts.  The  last  change  is  the  most 
important  one  effected  by  a  machine.  When  the  machine 
causes  the  power  to  act  upon  the  resistance  at  a  slower  rate 
than  it  would  were  it  applied  directly  to  it,  there  is  a  gain  of 
power ;  and  when  it  causes  it  to  act  upon  it  at  a  quicker  rate, 
there  is  a  loss  of  power.  When  the  machine  does  not  change 
the  rate,  there  is  neither  gain  nor  loss  of  power. 


NATURAL    PHILOSOPHY.  41 

QUESTIONS  ON   THE   GENERAL   LA  IV  OF  MACHINES. 

43.  In  a  machine,  the  power  moves  25  inches  while  the 
weight  is  moving  35  inches.  What  weight  would  be  balanced 
by  63  pounds  of  power  ? 

If  we  denote  the  power  by  P,  the  weight  by  W,  the  velocity 
of  the  power  by  VP,  the  velocity  of  the  weight  by  V  W,  and  the 
distances  passed  over  by  the  power  and  weight,  respectively,  by 
DP  and  D  W,  then  we  shall  have,  in  the  above  example, 
VP  —      V  W 


W  =  45  pounds. 

44.  In  a  machine,  a  power  of  27  pounds  balances  a  weight  of 
45  pounds.     How  far  does  the  power  move  while  the  weight 
moves  60  inches? 

1*=~\W 
VP  =  %  VW 
DP  =  f  X  60  =  100  inches. 

45.  In  a  machine,  the  power  moves  56  inches  while  the  weight 
moves  21  inches.     What  power  will  balance  a  weight  of  600 
pounds  ? 

46.  In  a  machine,  the  power  moves  35  inches  while  the  weight 
is  moving  63  inches.     What  weight  will  be  balanced  by  250 
pounds  of  power  ? 

47.  In  a  machine,  the  power  moves  15  centimetres  while  the 
weight  moves  40  centimetres.    What  power  will  balance  a  weight 
of  90  grammes  ? 

48.  In  a  machine,  the  power  moves  24  centimetres  while  the 
weight  is  moving  56  centimetres.     What  weight  would  be  bal- 
anced by  1  30  grammes  of  power  ? 

49.  In  a  machine,  a  power  of  28  pounds  balances  a  weight  of 
49  pounds.     How  far  will  the  power  move  while  the  weight  moves 
20  inches  ? 

50.  In  a  machine,  a  power  of  40  pounds  balances  a  weight  of 
32  pounds.     How  far  will  the  weight  move  while  the  power  is 
moving  30  inches  ? 

51.  In  a'machine,  a  power  of  50  grammes  balances  a  weight 


ELEMENTS    OF 


of  80  grammes.     How  far  will  the  power  move  while  the  weight 
is  moving  15  centimetres  ? 

52.  In  a  machine,  a  power  of  81  grammes  balances  a  weight 
of  63  grammes.  How  far  will  the  weight  move  while  the  power 
is  moving  25  centimetres  ? 

69.   The  Lever.  —  The  lever  is  a  rigid  bar,  capable  of  turn- 
ing upon  a  fixed  point  or  axis.    The  point  on  which  the  lever 
Fig.  28.  turns  is  called  \hefulcrum. 

Different  forms  of  the  lever  are 
shown  in  Figure  28.  F  is  the 
fulcrum,  W  the  weight,  and  P  the 
power. 

When  the  fulcrum  is  between 
the  power  and  weight,  the  lever  is 
said  to  be  of  \htfirst  order ;  when 
the  weight  is  between  the  fulcrum 
and  power,  the  lever  is  said  to  be 
of  the  second  order ;  and  when  the  power  is  between  the 
fulcrum  and  weight,  the  lever  is  said  to  be  of  the  third 
order. 

Fig.  29.  Fig.  30. 

W 


A  bar  used  for  raising  a  weight  is  a  lever.     When  it  is  used 
as  shown  in  Figure  29,  it  is  a  lever  of  the  first  order.     When  it 
Fig.  3 1.  is  used  as  shown  in  Figure  30,  it  is  a 

lever  of  the  second  order.  A  fishing- 
rod  (Figure  31)  is  a  lever  of  the  third 
order. 

The  arms  of  a  lever  are  the  distances  from  the  fulcrum  to 
the  points  where  the  power  and  weight  are  applied,  in  case  the 
lever  is  straight ;  or  the  distances  from  the  fulcrum  to  the 
lines  which  show  the  direction  of  the  power  and  weight,  in 
case  the  lever  is  bent. 


NATURAL    PHILOSOPHY.  43 

In  Figure  28,  FP  is  in  each  case  the  power  arm,  and  F  W 
the  weight  arm.  In  Figure  32  the  dotted  Fig.  32. 

lines,  which  are  supposed  to  be  drawn 
from    the    fulcrum    perpendicularly    to 
the  directions  in  which  the  weight  and  a 
power  act,  are  the  arms  of  the  bent  lever,  abfc. 

70.  The  Special  Law  of  the  Lever.  —  The  special  law  of 
the  lever  is  that  the  velocities  of  the  power  and  weight  are  in 
the  direct  ratio  of  the  lengths  of  the  arms  to  which  they  are 
applied ;  that  is,  if  one  arm  of  the  lever  is  three  times  as 
long  or  one  third  as  long  as  the  other,  the  power  or  weight 
applied  to  this  arm  will  move   three  times  as  fast  or  one 
third  as  fast  as  the  one  applied  to  the  other  arm. 

There  will  be  a  gain  of  power  in  the  lever  whenever  the 
power  arm  is  the  longer ;  for  the  power  will  then  move  the 
faster,  and  will  balance  a  weight  greater  than  itself.  There 
will  be  a  loss  of  power  when  the  power  arm  is  the  shorter ; 
for  the  power  will  then  move  the  slower,  and  will  balance 
a  weight  less  than  itself. 

In  a  lever  of  the  second  order  there  will  always  be  a  gain 
of  power,  and  in  a  lever  of  the  third  order  a  loss  of  power. 
In  the  lever  of  the  first  order  there  will  be  a  gain  or  loss  of 
power,  or  neither,  according  as  the  fulcrum  is  nearer  the 
weight,  or  nearer  the  power,  or  midway  between  the  two. 

71.  The  Compound  Lever.  —  Sometimes  two  or  more  simple 
levers   are   combined,  as   shown   in    Figure  33.     If  P  is  five 
times  as  far  from  the  fulcrum  f  Fig.  33. 

as   A    is,  the  point  P  will  then 

move  five  times  as  fast  as  the 

point  A,  and  a  pull  of  one  pound 

on  P  will  exert   a  pull  of   five 

pounds  on  A.    If  B  is  five  times 

as  far  from  the  fulcrum  F  as  W 

is,  the  five  pounds  of  pull  on  B  will  exert  twenty-five  pounds  of 

pull  at    W.     In  this  case  one  pound  of  pull  exerted  at  P  will 

balance  twenty-five  pounds  at    \V ;  but  it  would  be  found  on 


44  ELEMENTS    OF 

trial  that  by  pulling  P  down  one  inch,  W  would  be  raised  only 
one  twenty-fifth  of  an  inch. 

Such  a  combination  of  levers  is  called  a  compound  lever. 

QUESTIONS   ON   THE   LEVER. 

53.  In  a  lever,  the  power  arm  is  18  inches  and  the  weight 
arm  is  42  inches.  What  weight  would  be  balanced  by  60  pounds 
of  power  ? 

Denote  the  power  arm  by  P  A,  and  the  weight  arm  by  W  A. 
=%  W  A 
=  \  VW 
—     W 


W  '=  25!"  pounds. 

54.  In  a  lever,  the  power  arm  is  36  inches,  and  the  weight 
arm  27  inches.   What  power  will  balance  a  weight  of  75  pounds  ? 

55.  In  a  lever,  the  power  arm  is  14  decimetres  long,  and  the 
weight  arm  21  decimetres.     What  weight  would  be  balanced  by 
70  grammes  of  power  ? 

56.  In  a  lever,  the  power  arm  is  49  decimetres  long,  and  the 
weight  arm  28  decimetres.     What  power  would  balance  a  weight 
of  17  kilogrammes  ? 

57.  In  a  lever,  a  power  of  30  pounds  balances  a  weight  of 
50  pounds,  and  the  power  arm  is  80  inches  long.     What  is  the 
length  of  the  weight  arm  ? 

58.  In  a  lever,  a  power  of  70  pounds  balances  a  weight  of 
20  pounds,  and  the  weight  arm  is  30  inches  long.     What  is  the 
length  of  the  power  arm  ? 

59.  In  a  lever,  a  power  of  150  grammes  balances  a  weight  of 
250  grammes,  and   the  power  arm   is   18  decimetres  in  length. 
What  is  the  length  of  the  weight  arm  ? 

60.  In  a  lever  of  the  first  order,  a  power  of  30  pounds  bal- 
ances a  weight  of  40  pounds,  and  the  power  arm  is  27  inches 
long.     What  is  the  length  of  the  lever  ? 

61.  In  a  lever  of  the  first  order,  a  power  of  55  grammes  bal- 
ances a  weight  of  35  grammes,  and  the  weight  arm  is  13  deci- 
metres long.     What  is  the  length  of  the  lever  ? 


NATURAL    PHILOSOPHY. 


45 


62.  In  a  lever  of  the  second  order,  the  length  of  the  lever  is 
65  decimetres,  and  a  power  of  24  grammes  will  balance  a  weight 
of  64  grammes.     What  is  the  length  of  the  weight  arm  ? 

63.  In  a  lever  of  the  third  order,  the  length  of  the  lever  is 
28  decimetres,  and  the  length  of  the  power  arm  is  12  decime- 
tres.    What  power  will  balance  18  grammes  of  weight? 

72.  The  Pulley.  —  The  pulley  is  a  small  Fig.  34. 
grooved  wheel  turning  freely  in  a  frame  called 
the  block.  It  is  a  machine  in  which  power 
is  applied  to  do  work  by  means  of  a  cord 
instead  of  a  bar,  as  in  the  case  of  the  lever. 
The  wheel  of  the  pulley  serves  simply  to 
diminish  friction  at  the  points  over  which 
the  cord  is  drawn. 

In  Figure  34  the  block  of  the  pulley  D  C  is  fastened  to 
the  beam  above,  so  as  to  be  stationary,  while  the  block  of 


Fig.  35- 


Fig.  36. 


Fig.  37- 


the  pulley  A  B  is  free  to  move  up  and 
down.  The  former  is  called  a  fixed 
pulley ;  and  the  latter,  a  movable  pulley. 
A  fixed  pulley  serves  simply  to  change 
the  direction  in  which  the  power  acts. 
73.  Systems  of  Pulleys  with  one  Cord.  — 


46  ELEMENTS    OF 

In  Figures  35,  36,  and  37,  are  shown  systems  of  pulleys 
with  a  single  cord,  that  is,  in  which  one  cord  passes  over 
all  the  pulleys.  The  power  is  applied  to  the  end  of  the 
rope,  and  the  weight  is  attached  to  the  movable  block. 
In  the  first  case,  on  raising  the  movable  block  one  inch, 
three  inches  of  rope  will  be  released,  since  the  rope  comes 
three  times  to  that  block.  In  this  case  the  power  will 
move  three  times  as  fast  as  the  weight.  In  the  second 
case,  on  raising  the  movable  block  one  inch,  four  inches 
of  rope  will  be  released,  since  the  rope  comes  four  times 
to  this  block.  In  this  case  the  power  will  move  four  times 
as  fast  as  the  weight.  In  the  third  case  the  power  will 
move  six  times  as  fast  as  the  weight. 

The  special  law  of  a  system  of  pulleys  with  a  single 
rope  is  that  the  velocities  of  the  power  and  weight  are  in  the 
inverse  ratio  of  the  number  of  times  the  cord  comes  to  each. 
As  the  cord  always  comes  once  to  the  power,  the  power 
will  balance  a  weight  as  many  times  itself  as  the  cord 
comes  times  to  the  block  bearing  the  weight. 

QUESTIONS  ON  PULLEYS  WITH  SINGLE  ROPE. 

64.  In  a  system  of  pulleys  with  a  single  rope,  the  rope  comes 
13  times  to  the  block  bearing  the  weight.  What  weight  would 
be  balanced  by  75  pounds  of  power  ? 

65.  In  a  system  of  pulleys  with  a  single  cord,  the  cord  comes 
9  times  to  the  block  bearing  the  weight.     What  power  would 
balance  19  grammes  of  weight  ? 

66.  In  a  system  of  pulleys  with  a  single  rope,  a  power  of  13 
pounds  balances  a  weight  of  91  pounds.     How  many  times  does 
the  rope  come  to  the  block  bearing  the  weight  ? 

67.  In  a  system  of  pulleys  with  a  single  rope,  a  power  of  72 
grammes  balances  a  weight  of  792  grammes.     How  many  times 
does  the  rope  come  to  the  block  bearing  the  weight  ? 

74.  Systems  of  Pulleys  with  more  than  one  Rope.  —  The  law 
of  the  pulley  is  sometimes  stated  as  follows  :  A  stretched  rope 
must  have  the  same  tension  throughout  its  whole  length. 


NATURAL    PHILOSOPHY. 


47 


Figure  38  represents  a  system  of  pulleys  in  which  two  ropes 
are  used.     Here  a  weight  of  four  pounds  is  balanced  by  a  power 
Fig.  38.     of  one  pound.     The  parts  of  the  rope         Fig.  39. 
A  D  and  A  B  must  each  have  a  ten- 
sion equal  to  the  power.     The  rope 
A  rebalances  the  two  tensions,  #/> 
and  £  A,  and  must  therefore  have  a 
2  tension  of  twice  the  power.  The  three 
tensions    supporting    the    pulley    A 
|>)  amount  therefore   to   four  times   the 
i    power. 

i        In  the  system  shown  in  Figure  39 
p  four  ropes  are  used.     The  tensions  of  8 

the  several  ropes  will  be  readily  un- 
4Aw       derstood  from  the  numbers.     It  will 
be  seen  that  in  this  case  the  power  is 
doubled  by  each  movable  pulley  which  is  added ;  but,  as  in  all 
the  systems  we  have  examined,  what  is  gained  in  power  is  lost 
in  speed. 

75.  Wheel  and  Axle.  —  The  wheel  and  axle  (Figure  40) 
consists  of  a  wheel,  or  drum,  #,  mounted  on  an  axle  b. 
The  power  and  weight  are  applied  Fig.  40. 

to  ropes  which  pass,  one  over  the 
wheel  and  the  other  over  the  axle, 
in  opposite  directions,  so  that  one 
unwinds  as  the  other  winds  up.  The 
power  and  weight  are  really  applied 
to  the  wheel  and  axle  at  the  point 
where  the  rope  touches  each,  that  is, 
at  the  end  of  the  radius  of  each.  The  one  applied  to  the 
wheel  moves  the  faster,  and  just  as  many  times  faster  as 
the  circumference  or  the  radius  of  the  wheel  is  times  the 
circumference  or  the  radius  of  the  axle. 

The  special  law  of  the  wheel  and  axle  is  that  the  veloci- 
ties of  the  power  and  weight  are  in  the  direct  ratio  of  the  radii 
to  whicti  they  are  applied.  When  the  power  is  applied  to 


V 


ELEMENTS   OF 


the  wheel,  there  is  a  gain  of  power ;  and  when  it  is  applied 
to  the  axle,  there  is  a  loss  of  power. 

The  chief  use  of  the  wheel  and  axle  in  machinery  is  in 
transmitting  rotary  motion  from  one  piece  to  another,  with  or 
without  a  change  of  velocity.  For  an  increase  of  velocity,  a 
large  wheel  must  act  upon  a  small  one;  and  for  a  diminution  of 
velocity,  a  small  wheel  must  act  upon  a  large  one.  When  there 
is  to  be  no  change  of  velocity,  the  wheels  must  both  be  of  the 
same  size. 

76.  Cog-Wheels.  —There 
are  various  ways  in  which  the 
axle  of  one  wheel  is  made 
to  act  on  the  circumference 
of  another.  Sometimes  the 
one  turns  the  other  by  rub- 
bing against  it,  or  by  friction. 
The  most  common  way, 
however,  is  by  means  of 
teeth  or  cogs  raised  on  the 
surfaces  of  the  wheels  and 
axles.  The  cogs  on  the 
wheel  are  usually  called  teeth, 
while  those  on  the  axle  are  called  leaves,  and  the  part  of  the 
axle  from  which  they  project  is  called  tis\t  pinion. 

77.  The  Gain  of  Power  by  Wheel- Work,  —in  the  train  of 
wheels  in  Figure  41,  if  the  circumference  of  the  wheel  a  is  36 
inches,  and  that  of  the  pinion  b  is  9  inches,  or  one  fourth  as 
great,  a  power  of  one  pound  at  P  will  exert  a  force  of  four 
pounds  on  b.  If  the  circumference  of  the  wheel  e  is  30  inches, 
and  that  of  the  pinion  C  10  inches,  the  four  pounds  acting  on 
the  former  will  exert  a  force  of  twelve  pounds  on  the  latter.  If 
the  circumference  of  the  wheel  f  is  40  inches,  and  that  of  the 
axle  d  8  inches,  the  twelve  pounds  acting  on/"  will  exert  a  force 
of  sixty  pounds  on  d.  One  pound  at  P  will  then  balance  sixty 
pounds  at  W. 

But  in  this  case,  as  in  all  others,  what  is  gained  in  power  is 
lost  in  speed  ;  since  the  one  pound  at  P  must  move  througli 
sixty  inches  in  order  to  raise  the  sixty  pounds  at  W  one  inch. 


NATURAL     PHILOSOPHY. 


49 


78.  Belted  Wheels.  —  Another  way  in  which  wheels  and  axles 
may  be  made  to  act  upon  one  another  is  by  means  of  a  belt,  or 
band,  passing  over  them  both.  They  may  thus  be  at  any  dis- 
tance apart,  and  may  turn  either  the  same  way  or  contrary  ways, 


Fig.  42. 


Fig.    43- 


according  as  the  belt  does  or  does  not  cross  between  them  (Fig- 
ures 42  and  43).  A  cog-wheel  and  its  pinion  must,  of  course, 
always  turn  in  contrary  directions. 

79.  The  Windlass  and  Capstan.  —  The  windlass  is  a  hori- 
zontal barrel  turned  by  means  of  a  Fig.  44 

crank  or  spokes  (Figure  44).  It 
may  be  regarded  as  a  modification 
of  the  wheel  and  axle,  the  crank 
taking  the  place  of  the  wheel.  The 
capstan  is  an  upright  drum  turned 
by  means  of  levers,  which  may  be 
removed  at  pleasure. 

QUESTIONS  ON  THE  WHEEL  AND  AXLE. 

68.  The  radius  of  a  wheel  is  40  inches,  and  that  of  its  axle 
15  inches.  What  weight  on  the  axle  would  be  balanced  by  50 
pounds  of  power  on  the  wheel  ? 

Denote  the  radius  of  the  wheel  by  R  W,  and  that  of  the  axle 
by  R  A. 

RW=\  RA 

vp—\  vw 

P  =     W 


50-5-  I  = 

W=.  133^  pounds. 

69.  The  radius  of  a  wheel  is  18  decimetres,  and  that  of  its 
axle  12  cl&ci  metres.  What  weight  on  the  wheel  would  be  bal- 
anced by  32  grammes  of  power  on  the  axle  ? 

4 


50  ELEMENTS    OF 

70.  In  a  wheel  and  axle,  a  power  of  63  pounds  on  the  axle 
balances  a  weight  of  35  pounds  on  the  wheel.     The  radius  of 
the  wheel  is  16  decimetres.     What  is  the  radius  of  the  axle  ? 

71.  A  power  of  21  pounds  on  the  wheel  balances  a  weight  of 
77  pounds  on  the  axle.     The  radius  of  the  axle  is  5  inches. 
What  is  the  radius  of  the  wheel  ? 

80.  The  Inclined  Plane.  —  An  inclined  plane  is  simply  an 
inclined  surface.      It   is    easier  to  roll   a  body  up  an    in- 
clined surface  than  to  raise  the  body  vertically  to  the  same 
height.     The  reason  is  obvious.     The  body  must  be  raised 
against  the  action  of  gravity  ;  and^by  rolling  the  body  up 
the  inclined  surface,  the  power  is  compelled  to  act  through 
a  distance  equal  to  the  length  of  the  surface  in  raising  the 
weight  the  height  of  it. 

The  special  law  of  the  inclined  plane  is  that  the  velocities 
of  the  power  and  weight  are  in  the  ratio  of  the  length  of  the 
plane  to  its  height.  Since  the  power  and  weight  are  in  the 
inverse  ratio  of  their  velocities,  it  follows  that  the  power 
will  be  to  the  weight  as  the  height  of  the  plane  is  to  its  length. 

The  law  of  the  inclined  plane  may  be  demonstrated  by  means 
Fig.  45.  of  the  apparatus  represented  in 

Figure  45.  R  S  is  a  smooth 
piece  of  hard  wood  hinged  at 
R ;  by  means  of  a  screw  it 
can  be  clamped  at  any  angle  x 
against  the  curved  support ;  a 
is  a  metal  cylinder,  to  the  axis 
of  which  is  attached  a  string 
passing  over  a  pulley  to  a 
scale-pan  P. 

It  is  thus  easy  to  ascertain  by  direct  experiments  what  weight 
must  be  placed  in  the  pan  P  in  order  to  balance  a  roller  of  any 
given  weight. 

The  line  R  S  represents  the  length,  S  T  the  height,  and  R  T 
the  base  of  the  inclined  plane. 

8 1.  The  Wedge.  —  Instead  of  lifting  a  weight  by  moving 


NATURAL    PHILOSOPHY. 


it  along  an  inclined  plane,  we  may  do  the  same  thing  by 

pushing  the   inclined  plane  under   the  weight.       F;     6 

When  used  in  this  way  the  inclined  plane  is 

called   the  wedge.      A  wedge   which   is  used 

for  splitting  wood  has  usually  the  form  of  a 

double  inclined  plane,  as  in  Figure  46.     The 

law  of  the  wedge  is  the  same  as  that  of  the 

inclined  plane ;  but  since  a  wedge  is  usually 

driven  by  a  blow  instead  of  a  force   acting 

continuously,  it   is  difficult   to  illustrate  this 

law  by  experiments. 

The  wedge  is  especially  useful  when  a  large  weight  is  to  be 
raised  through  a  very  short  distance.  Thus,  a  tall  chimney,  the 
foundation  of  which  has  settled  on  one  side,  has  been  made  up- 
right again  by  driving  wedges  under  that  side.  So,  too,  ships 
are  often  raised  in  docks  by  driving  wedges  under  their  keels. 
Cutting  and  piercing  instruments,  such  as  razors,  knives,  chisels, 
awls,  pins,  needles,  and  the  like,  are  different  forms  of  wedges. 

82.  The  Screw.  —  In  Figure  47  we  have  a  machine 
called  the  screw.  It  is  a  movable  inclined  plane,  in  which 
the  inclined  surface  winds  round  a 
cylinder.  The  cylinder  is  the  body 
of  the  screw,  and  the  inclined  sur- 
face is  its  thread. 

The  screw  usually  turns  in  a 
block  N,  called  the  ;////.  Within 
the  nut  there  are  threads  exactly 
corresponding  to  those  on  the 
screw.  The  threads  of  the  screw 
move  in  the  spaces  between  those 
of  the  nut. 

The  power  is  usually  applied  to 

the  screw  by  means  of  a  lever  P.  Sometimes  the  screw  is 
fixed  and  the  nut  is  movable,  and  sometimes  the  nut  is 
fixed  and  the  screw  movable. 


ELEMENTS   OF 


83.   The  Endless   Screw.  —  In  Figure  48  the  thread  of  the 
Fig.  48.  screw    works    between    the     teeth    of    the 

wheel  ;  hence,  if  the  screw  is  turned, 
the  wheel  must  turn.  Since  as  fast  as  the 
teeth  at  the  left  escape  from  the  screw  those 
on  the  right  come  up  to  it,  the  screw  is  act- 
ing upon  the  wheel  continually  ;  hence  this 
machine  is  called  the  endless  screw. 


NATURAL    PHILOSOPHY.  53 


III. 

PHYSICS. 

I. 
STATES    OF   MATTER. 

A.   THREE  STATES  OF  MATTER. 

84.  The  Three  States.  —  Matter  exists  in  three  different 
states,  known  as  the  solid,  the  liquid,  and  \hegaseous.     Ice 
is  a  solid,  water  is  a  liquid,  and  steam  and   air  are  gases. 
While  the  substance  of  a  body  depends  upon  its  atomic 
structure  (2),  the  state  of  a  body  depends  upon  its  mo- 
lecular structure.     Hence  the  state  of  matter  is  a.  physical 
condition,  and  changes  of  state  are  physical  changes. 

85.  Cohesion  in  the   Different  States  of  Matter.  —  The 
different  states  of  matter  depend  upon  the  strength  of  the 
attraction  of  cohesion  among  the  molecules.     This  is  compara- 
tively strong  in  solids,  very  weak  in  liquids,  and  entirely 
wanting  in  gases. 

The  molecules  of  some  solids  are  bound  together  much  more 
firmly  than  those  of  others  by  cohesion  ;  but  even  when  this 
bond  is  weakest,  the  molecules  manifest  a  disposition  to  main- 
tain their -relative  positions  in  the  body,  and  the  body  to  preserve 
its  form.  In  liquids  the  bond  of  cohesion  is  so  slight  that  the 
molecules  manifest  no  disposition  to  maintain  their  relative  posi- 
tions in  the  body,  nor  does  the  body  tend  to  preserve  its  form. 
Gases  are  not  held  together  at  all  by  cohesion,  but  only  by  gravity. 

86.  Molecular  Motion  in  the  Different  States  of  Matter.  — 


54  ELEMENTS   OF 

The  molecules  are,  undoubtedly,  in  incessant  motion  in  every 
state  of  matter,  but  their  freedom  of  motion  is  very  different  in 
the  different  states.  In  so/ids,  the  molecules,  when  left  to  them- 
selves, have  fixed  positions,  within  which  they  can  move  to  a 
limited  extent,  but  from  which  they  can  never  escape.  When 
left  to  themselves,  the  molecules  of  a  solid  never  move  around 
among  themselves  so  as  to  change  their  relative  positions.  A 
molecule  in  the  interior  can  never  work  its  way  to  the  surface, 
nor  can  one  at  the  surface  work  its  way  into  the  interior. 

In  liquids,  the  molecules  are  all  the  time  moving  about  among 
themselves  in  the  interior  of  the  mass  with  the  utmost  freedom. 
No  molecule  is  confined  within  particular  limits  within  the  mass, 
but  every  molecule  is  continually  moving  to  and  fro  in  every  direc- 
tion throughout  the  entire  mass.  They,  however,  never  escape 
from  the  influence  of  cohesion.  So  long  as  they  are  in  the  in- 
terior of  the  mass,  the  cohesion  of  the  molecules  on  one  side  of 
them  is  exactly  balanced  by  that  of  the  molecules  on  the  other 
side  ;  hence  it  does  not  interfere  with  the  freedom  of  their  motion. 
But  as  the  molecules  come  to  the  surface,  they  experience  only 
the  pull  of  the  molecules  behind  them,  and  this  is  usually  suffi- 
cient to  stop  their  outward  motion  and  to  cause  them  to  return 
into  the  interior  of  the  mass. 

In  gases,  the  molecules  are  moving  without  the  slightest 
restraint  from  cohesion  ;  hence  they  move  in  straight  lines. 
They  are  continually  striking  together  and  rebounding  again, 
but  after  each  rebound  they  move  in  straight  lines  till  they 
encounter  other  molecules.  There  is  no  force  acting  within  the 
mass  of  a  gas  which  tends  to  check  the  motion  of  the  molecules 
at  any  point  ;  hence  gases  do  not,  like  liquids,  tend  to  assume  a 
definite  surface. 

87.  The  Distances  between  the  Molfcules  in   the  Different 
States  of  Matter.  —  As   a   rule,  the    molecules    are  nearer  to- 
gether in  solids  than  in  liquids,  and  in  liquids  than  in  gases. 
The  molecules  of  steam  are  about  seventeen  hundred  times  as 
far  apart  as  those  of  water. 

88.  Behavior  of  the  Different  States  of  Matter  when  Small 
Portions  of  each  are  placed  in   Empty    Vessels.  —  If  a  small 
portion  of  a  solid  is  placed  in  an  empty  vessel,  it  will  either  not 
conform  to  the  shape  of  the  vessel  at  all,  or,  in  the  case  of  a  soft 


NATURAL    PHILOSOPHY.  55 

solid,  only  slowly  and  imperfectly.  This  is  owing  to  the  ten- 
dency of  a  solid  to  maintain  its  shape.  If  a  small  amount  of  a 
liquid  is  put  into  an  empty  vessel,  it  will  conform  at  once  and 
perfectly  to  the  shape  of  the  vessel,  but  it  will  not  completely 
till  it.  The  liquid  will  sink  to  the  lowest  part  of  the  vessel,  and 
will  be  separated  by  a  definite  surface  from  the  space  in  the 
upper  part  of  the  vessel.  This  is  because  the  cohesion  of  the 
liquid  checks  the  outward  motion  of  the  molecules,  and  so  keeps 
them  from  moving  away  from  the  mass.  If  any  portion  of  a.  gas, 
however  small,  is  placed  in  an  empty  vessel,  however  large,  the 
gas  will  completely  fill  the  vessel.  This  is  because  there  is 
nothing  to  check  the  outward  motion  of  the  molecules  of  the 
gas,  save  the  walls  of  the  vessel  in  which  it  is  enclosed. 

B.   FLUIDS. 

89.  Fluids.  —  Owing  to  their  freedom  of  molecular  mo- 
tion, liquids  and  gases  have  several  characteristics  in  common. 
They  are,   accordingly,    often    classed   together  as  fluids. 
This  appellation  is  derived  from  the  readiness  with  which 
portions  of  each   of  these  states  of  matter  flow  over  or 
among  each  other. 

90.  Pascal's  Law.  —  One  of  the  most  remarkable  char- 
acteristics of  a  fluid  is  the  way  in  which  it  transmits  any 
pressure  that  is  brought  to  bear  on  it.     If  any  pressure  is 
brought  to  bear  on  any  portion  of  the  surface  of  a  fluid  which 

fills  a  closed  vessel,  a  pressure  just  equal  to  it  will  be  trans- 
mitted through  the  fluid  to  every  equal  portion  of  surface. 
This  law  was  enunciated  by  Pascal,  and  is  known,  as 
Pascal's  law. 

The   following  experiment    shows   that    pressure   is   trans- 
mitted  in   all   directions  by  a  Fig.  49. 
fluid.      A  tube  (Figure   49)  is 
provided  with  a  piston  and  fit- 
ted with  a  hollow  globe,  which 
is   pierced    with  a   number  of 
orifices,  arranged    in    a   circle 
around-it.     Fill  the  globe  and 


ELEMENTS    OF 


tube  with  water.    If  the  piston  is  pushed  in,  the  water  spouts  out 
of  all  the  orifices,  and  not  merely  those  opposite  the  piston. 

Conceive  a  vessel  of  any  form,  in  the  sides  of  which  are  a 
number  of  cylindrical  apertures,  all  of  the  same  size,  and  closed 
Fig.  50.  with  movable  pistons,  as  shown  at  A,  B,  C, 

D,  and  E  (Figure  50).  Suppose  a  pound  of 
pressure  brought  to  bear  upon  A.  A  pound 
of  pressure  will  be  transmitted  to  each  of  the 
other  pistons  in  the  direction  of  the  arrows. 
If  the  piston  B  has  only  half  the  surface  of 
A,  it  will  receive  only  y£  a  pound  of  pressure  ; 
if  it  has  twice  the  surface  of  A,  it  will  re- 
ceive 2  pounds  of  pressure  ;  if  it  has  three  times  the  surface  of  A, 
it  will  receive  3  pounds  of  pressure  ;  etc.  Hence,  by  means  of  a 
liquid,  a  small  pressure  upon  a  small  surface  may  be  made  to 
exert  a  great  pressure  upon  a  large  surface. 

91.   The  Hydraulic  Press.  —  In  Figure  51  we  have  two 


Fig.  51. 


cylinders,  with  a  piston  in 
each.  Suppose  that  the 
surface  of  the  larger  pis- 
ton is  fifty  times  that  of 
the  smaller ;  if  the  latter 
is  pressed  downward  by 
a  weight  of  one  pound, 
an  upward  pressure  of 
one  pound  will  be  brought  to  bear  upon  each  portion  of 
the  surface  of  the  large  piston  equal  to  that  of  the  small 
piston.  The  whole  upward  pressure  on  the  large  piston 
will  then  be  fifty  times  the  downward  pressure  on  the 
small  one.  If  the  surface  of  the  larger  piston  had  been 
one  hundred  times  that  of  the  smaller,  one  pound  on  the 
latter  would  have  balanced  one  hundred  on  the  former ; 
and  so  on. 

The  hydraulic  press  is  constructed  on  the  principle  just 
illustrated.  One  form  of  this  press  is  shown  in  Figures  52 
and  53.  The  two  cylinders  A  and  B  are  connected  by  the 


NATURAL    PHILOSOPHY. 


57 


pipe  d.  The  piston  #,  in  the  cylinder  A,  is  worked  by  the 
handle  O,  and  forces  water  into  the  large  cylinder  B, 
where  it  presses  up  the  piston  C.  If  the  end  of  the  pis- 
ton Cis  1000  times  as  large  as  that  of  the  piston  a,  a  pres- 
sure of  2  pounds  on  a  would  exert  a  pressure  of  2000 
pounds,  or  one  ton,  upon  C.  If  a  man,  in  working  the 

Fig.  52. 


handle  O,  forces  down  the  piston  a  with  a  pressure  of  50 
pounds,  he  would  bring  to  bear  upon  C  a  pressure  of 
25  tons. 

This  press  is  used  for  pressing  cotton,  hay,  cloth,  etc.,  into 
bales  ;  for  extracting  oil  from  seeds  ;  for  testing  cannon,  boilers, 
etc. ;  and  for  raising  ships  out  of  the  water. 


58  ELEMENTS    OF 

The  hydraulic  jack  is  a  form  of  the  hydraulic  press,  adapted 
to  raising  heavy  weights. 

92.  The  Principle  of  Archimedes.  —  A  body  in  a  fluid  is 
buoyed  up  by  a  force  equal  to  the  weight  of  tlie  fluid  it  dis- 
places. This  fact  was  discovered  by  Archimedes,  and  is 
therefore  designated  by  his  name. 

This  principle  may  be  verified  by  the  following  experiment. 
A  brass  cylinder  is  constructed  so  as  just  to  fill  a  cup.  The 
cup  and  cylinder  are  hung  from  one  pan  of  a  balance  (Figure 
54)  and  counterpoised  in  the  air  by  weights  in  the  other  pan. 

Fig    S3- 


The  cylinder  is  then  allowed  to  hang  in  a  vessel  of  water.  The 
weights  overbalance  the  cup  and  cylinder,  showing  that  the 
water  lifts  the  cylinder  up.  Equilibrium  is  restored  by  filling 
the  cup  with  water.  When  the  cup  is  full,  the  beam  of  the  bal- 
ance will  be  horizontal,  and  the  cylinder  will  be  completely  in 
the  water,  showing  that  the  cylinder  is  buoyed  up  by  the  water 
with  a  force  equal  to  the  weight  of  a  cupful  of  water,  or  to  the 
weight  of  the  water  displaced  by  the  cylinder. 

93.  Forces  acting  upon  a  Body  immersed  in  a  Fluid.  — 
Every  body  immersed  in  a  fluid  is  subjected  to  two  forces  : 
one  equal  to  its  own  weight,  which  tends  to  make  the  body 


NATURAL    PHILOSOPHY. 


59 


sink ;  the  other  equal  to  the  weight  of  the  liquid  displaced, 
which  tends  to  make  the  body  rise. 

When  a  body  displaces  more  than  its  own  weight  of  a 
Fig.  54. 


fluid,  it  will  rise  in  that  fluid  ;  when  it  displaces  less  than 
its  own  weight,  it  will  sink ;  and  when  it  displaces  just 
its  own  weight,  it  will  remain  suspended  wherever  it  happens 
to  be. 

Fig.  55- 


These  three  cases  may  be  illustrated  by  putting  an  egg  into 
salt  and  fresh  water  (Figure  55).  When  the  egg  is  placed  in 
salt  water,  it  rises  to  the  surface  because  it  displaces  more  than 
its  own  weight  of  the  brine.  When  it  is  put  into  the  fresh 


6o 


ELEMENTS    OF 


water,  it  sinks  to  the  bottom  because  it  displaces  less  than  its 
own  weight  of  the  water.     When  it  is  put  into  a  proper  mixture 
Fig.  56.  of  fresh  water  and  brine,  it  will 

remain  suspended  in  the  fluid, 
because  it  displaces  just  its  own 
weight  of  the  mixture. 

94.   Floating  Bodies.  —  Every 
body  floating  in  a  fluid  displaces 
just  its  own  weight  of  the  fluid. 
This  is  equally  true   of  a  ship 
floating  in  water,  or  a  balloon 
floating  in  the  air  (Figure  56). 
The  more  heavily   the   ship  is 
loaded,    the   deeper   she    sinks 
into    the   water.      By   throwing 
out  the  sand  which  is  used  as 
ballast,    the    balloon    is    made 
lighter,  so  as  to  displace  more 
than  its  own  weight  of  air.     It 
»'"  then    rises    till    it    comes    into 
more  highly  rarefied  air,  where  it  displaces  just  its  own 
weight,  when  it  again  floats  along  at  the  same  level.     If 
Fig.  57.  some  of  the  gas  is  allowed  to  escape, 

the  balloon  becomes  less  in  bulk,  and 
so  displaces  less  than  its  own  weight 
of  air.  It  then  sinks  until  it  again 
displaces  its  own  weight. 

The  appendage  at  the  side  of  the  bal- 
loon (Figure  56)  is  called  a  parachute, 
and  can  be  used  in  descending  from  the 
balloon.  It  consists  of  a  large  circular 
piece  of  cloth  (Figure  57)  about  16  feet 
in  diameter,  which,  by  the  resistance  of 
the  air,  spreads  out  like  a  gigantic  um- 
brella. In  the  centre  there  is  an  aperture,  through  which  the 
air,  compressed  by  the  rapidity  of  the  descent,  makes  its  escape  ; 


NATURAL    PHILOSOPHY. 


61 


for  otherwise  oscillations  might  be  produced,  which  would  be 
dangerous  to  the  aeronaut. 

In  Figure  56  the  parachute  is  attached  to  the  network  of  the 
balloon  by  means  of  a  cord,  which  passes  round  a  pulley,  and 
is  fixed  at  the  other  end  to  the  boat.  When  the  cord  is  cut  the 
parachute  sinks,  at  first  very  rapidly,  but  more  slowly  as  it  be- 
comes distended,  as  represented  in  the  figure. 

95.  Method  of  finding  the  Specific  Gravity  of  Solids  and 
Liquids.  —  To  find  the  specific  gravity  (53)  of  a  solid  or 
liquid,  it  is  necessary  to  find the  weight  of  a  volume  of  water 

Fig.  58.  Fig.  59. 


equal  to  that  of  a  portion  of  the  solid  or  liquid  whose  specific 
gravity  is  to  be  found.  By  means  of  the  principle  of  Ar- 
chimedes, the  weight  of  this  volume  of  water  is  easily  found. 

Suppose  we  wish  to  find  the  specific  gravity  of  copper. 
Fasten  the  piece  of  copper  to  one  pan  of  the  balance  by  a  fine 
thread  (Figure  58),  and  counterpoise  it  in  the  air  with  weights 
in  the  other  pan.  Suppose  it  to  weigh  125.35  grains.  Then 
suspend  it  in  a  vessel  of  water  and  restore  the  equilibrium  by 
placing  weights  in  the  pan  supporting  the  copper.  Suppose  it 
to  require  14.24  grains.  This,  according  to  the  principle  of 


62 


ELEMENTS    OF 


Archimedes,  is  the  weight  of  the  water  displaced  by  the  copper, 
or  of  a  volume  of  water  equal  to  that  of  the  copper.  The 
specific  gravity  of  the  copper  is  then  ^f.^f  =  8.8. 

When  the  body  whose  specific  gravity  we  wish  to  find  is 
lighter  than  water,  we  must  fasten  it  to  a  heavy  body  to  sink  it. 
We  then  find,  by  the  above  method,  the  weight  of  the  water 
displaced  by  the  sinker  alone,  and  by  the  sinker  and  light  body 
together.  The  difference  between  the  two  will  be  the  weight 
of  the  water  displaced  by  the  lighter  body. 

The  specific  gravity  of  a  liquid  may  be  found  by  the  follow- 
ing method.  A  glass  ball,  weighted  with  mercury  inside,  is  first 
accurately  weighed  in  air.  It  is  then  immersed  in  a  vessel  of 
alcohol  or  other  liquid  under  examination  (Figure  59),  and 
equilibrium  is  restored  by  adding  weights  to  the  pan  from  which 
the  ball  is  suspended.  Suppose  35.43  grains  are  required. 
This  will  be  the  weight  of  the  ball's  volume  of  alcohol.  Next 
immerse  the  ball  in  water,  and  restore  the  equilibrium  as  before. 
Suppose  it  requires  44.28  grains  this  time.  This  will  be  the 
weight  of  the  ball's  volume  of  water.  The  specific  gravity  of 
alcohol  will  be  f  f  ;|f  ==  .8. 

96.  The  Hydrometer. — A  hydrometer  is  an  instrument  for 
finding  the  specific  gravity  of  liquids.  Common  forms  of  it  are 

shown  in  Figure  60.  They  are 
weighted  at  the  lower  end  with 
mercury  to  keep  them  in  an  up- 
right position.  The  bulb  above 
the  mercury  causes  them  to  dis- 
place enough  of  a  liquid  to  float 
in  it.  When  put  in  a  liquid  they 
sink  in  it  till  they  displace  their 
own  weight.  The  deeper  they 
sink  in  a  liquid,  the  less  its  spe- 
cific gravity.  Their  stems  are 
graduated  in  such  a  way  that  the 
number  on  the  stem  at  the  sur- 
face of  the  liquid  indicates  the 
specific  gravity  of  the  liquid. 
This  is  a  convenient,  but  not  very  accurate  method  of  ascertain- 
ing the  specific  gravity  of  a  liquid. 


Fig.  60. 


NATURAL    PHILOSOPHY. 


Fig.  61. 


C.  GASES. 

97.  Expansibility  of  Gases.  —  One  of  the  most  marked 
characteristics  of  a  gas  is  its  capacity  for  indefinite  expan- 
sion. The  tendency  of  a  gas  to  expand  may  be  illustrated 
by  means  of  an  india-rubber  bag  partially  filled  with  air, 
closed  air-tight,  and  placed  under  the  receiver  of  an  air- 
pump.  When  the  air  is  exhausted  from  the  receiver,  the 
bag  fills  out,  as  shown  in  Figure  6 1 . 

The  tendency  of  a  gas  to  expand  is  due  to  two  facts,  namely, 
that  the  molecules  of  a  gas  are  not  held  together  by  cohesion 
(85),  and  that  they  are  moving  rapidly  in  straight  lines  (86). 
The  condition  of  a  gas  in  a 
closed  vessel  has  been  likened 
to  that  of  a  swarm  of  bees  in 
a  closed  room,  when  all  the 
bees  are  flying  at  random  in 
straight  lines.  They  would 
be  constantly  flying  against 
one  another  and  against  the 
walls  of  the  room.  It  has 
been  calculated  that  the  mole- 
cules of  air  are  moving  at  the 
average  rate  of  about  1600 
feet  a  second.  This  velocity  would  be  sufficient  to  carry  a  body 
in  a  vacuum  some  40,000  feet,  or  about  7  miles  high.  Now  the 
molecules  of  air  in  the  rubber  bag  are  all  the  time  flying  against 
one  another  and  against  the  bag  with  this  enormous  velocity. 
They  therefore  tend  to  expand  the  bag.  So  long  as  there  was 
air  in  the  receiver  outside  the  bag,  the  blows  against  the  bag 
from  within  were  met  and  balanced  by  an  equal  number  ol 
blows  from  without  ;  but  as  the  air  was  exhausted  from  the 
receiver,  there  were  fewer  and  fewer  blows  upon  the  bag  deliv- 
ered by  the  molecules  on  the  outside,  and  hence  the  bag  began 
to  yield  to  the  more  numerous  blows  from  within. 

98.   The  Diffusion  of  Gases.  —  When  any  two  gases  are 
brought  into  contact,  they  rapidly  mix  with  each  other. 


64  ELEMENTS    OF 

This  mixture  of  gases  when  brought  into  contact  is  called  dif- 
fusion. It  is  due  to  the  fact  that  the  molecules  are  far 
apart  and  in  constant  motion.  The  molecules  of  the  one 
gas  quickly  move  into  the  spaces  among  the  molecules  of 
the  -other  gas. 

99.  The  Expansive  Power  of  a  Gas  increased  by  Heat. — 
A  bulb  with  a  tube  projecting  from  it  is  placed  in  a  vessel 
of  water  so  that  the  open  end  of  the  tube  is  under  water,  as 
shown  in  Figure  62.  If  the  bulb  is  heated,  the  air  in  it  will 
expand  so  as  to  drive  out  a  portion  of  it  through  the  water. 
Heat  always  increases  the  expansive  power  of  a  gas.  This  is 
Fig.  62.  because  heat  causes  the  molecules  to 

fly  about  with  greater  velocity,  and 
therefore  with  greater  energy. 

100.  The  Expansive  Power  of  a  Gas 
increased  by  an  Increase  of  Pressure.  — 
An  increase  of  pressure  in  a  gas  in- 
creases its  expansive  power.  This  is 
because  the  increased  pressure  crowds 
the  molecules  nearer  together,  so  that 
there  are  more  molecules  in  the  same  space  to  beat 
against  the  enclosure.  In  the  cylinder  of  the  steam-engine 
the  steam  is  kept  at  a  high  temperature  and  under  great 
pressure. 

1 01.  The  Three  Laws  of  Gases. — Equal  volumes  of  all 
gases,  at  the  same  temperature  and  under  the  same  pressure, 
contain  the  same  number  of  molecules.  This  is  Avogadro's 
law. 

The  volume  of  a  confined  mass  of  gas  varies  inversely  as  the 
pressure  to  which  it  is  exposed.  The  less  the  pressure  the 
greater  the  volume,  and  the  greater  the  pressure  the  less 
the  volume.  This  is  Mariotte's  law.  This  law  might  be 
stated  thus  :  the  number  of  molecules  of  a  gas  in  a  given 
space,  and  the  expansive  power  of  the  gas,  vary  directly  as 
the  pressure  to  which  the  gas  is  exposed. 


NATURAL    PHILOSOPHY.  65 

The  volume  of  a  gas  under  constant  pressure  varies  directly 
as  the  absolute  temperature  of  the  gas.  This  is  Charles  s 
law. 

By  absolute  temperature  is  meant  temperature  measured  from 
a  point  459°  below  the  ordinary  zero.  The  temperature  indi- 
cated by  an  ordinary  thermometer  may  be  converted  into  abso- 
lute temperature  by  adding  459°  to  it.  Thus,  a  temperature  of 
70°  on  our  scale  would  be  a  temperature  of  70°  +  459°  =  529°  on 
the  absolute  scale.  A  temperature  of  —  15°  on  our  scale  would 
be  a  temperature  of  459° -[-  ( —  15°)  =  444°  on  the  absolute  scale. 


102.  The  Air- Pump. — The  essential  parts  of  an  air- 
pump  are  shown  in  Figures  63  and  64.  There  is  a  flat 
plate  for  holding  the  receiver  E,  called  the  pump-plate.  It 
is  ground  perfectly  flat,  so  that  an  air-tight  joint  is  formed 
between  it  and  the  receiver  when  the  latter  is  placed  upon 
it.  A  tube  connects  the  pump-plate  with  the  cylinder,  in 
which  a  piston  is  moved  up  and  down  by  means  of  the 

5 


66 


ELEMENTS    OF 


handle.  There  is  a  little  valve  6*  in  the  piston,  pressed 
down  by  a  spiral  spring  above  it.  There  is  also  a  valve 
S'  at  the  bottom  of  the  barrel,  fastened  to  a  rod  which 
passes  through  the  piston  in  such  a  way  that  the  valve  is 
opened  when  the  piston  rises,  and  closed  when  the  piston 
is  pushed  down,  by  the  friction  of  the  rod  against  the  pis 
ton.  When  the  piston  is  drawn  up  the  valve  in  the  piston 
is  closed,  and  no  air  can  pass  from  above  the  piston  into 
the  space  below  it.  At  the  same  time  S'  at  the  bottom  of 
the  barrel  is  opened,  and  the  expansive  force  of  the  air  in 
the  receiver  E  causes  some  of  the  air  to  pass  out  through 
the  tube  into  the  barrel  below  the  piston.  When  the  pis- 
Fig.  64. 


ton  is  pushed  down  the  valve  S'  is  closed  by  the  friction  of 
the  rod,  and  the  valve  ,5"  is  opened  by  the  expansive  force 
of  the  air  below  it  as  the  air  becomes  compressed,  and  the 
air  in  the  barrel  below  the  piston  passes  above  it  again.  In 
this  way,  every  time  the  piston  is  moved  up  and  down,  a 
part  of  the  air  is  removed  from  the  receiver.  F  is  a  gauge 
for  showing  the  extent  of  the  exhaustion  ;  R  is  a  cock,  by 
means  of  which  the  receiver  and  the  barrel  may  be  put  into 
communication  with  each  other,  or  either  may  be  shut  off 
from  the  other,  and  be  put  into  communication  with  the 
external  air. 

There  are  many  different  forms  of  air-pumps  ;  but  with  none 
of  the  ordinary  pumps  is  it  possible  to  obtain  perfect  exhaustion. 


NATURAL    PHILOSOPHY. 


The  air  becomes  finally  so  attenuated  as  not  to  have  sufficient 
expansive  force  to  open  the  valve. 

103.  Pressure  of  the  Air.  —  The  pressure  of  the  air  may  be 
illustrated  by  the  following  experiments.  Place  a  small  bell-jar, 
open  at  both  ends,  on  the  plate  of  the  air-pump,  and  cover  the 
top  of  the  jar  with  the  palm  of  the  hand.  When  the  air  is  ex- 
hausted from  the  jar,  the  hand  is  pressed  firmly  down  upon  the 
mouth  of  the  jar.  This  is  an  illustration  of  the  downward  pres- 
sure of  the  air.  It  was  not  perceived  at  first,  because  the  down- 
ward pressure  of  the  air  upon  the  hand  was  balanced  by  the 
upward  pressure  of  the  air  within  the  jar. 

The  weight-lifter  (Figure  65)  serves  to  illustrate  the  upward 
pressure  of  the  air.  It  consists  of  a  cylinder  of  glass  or  metal, 
A  B,  with  a  piston  moving  up  and 
down  in  it,  air-tight.  The  cylinder 
is  closed  at  the  top  by  a  plate  C,  to 
which  may  be  screwed  a  tube  to 
connect  the  cylinder  with  the  air- 
pump.  The  cylinder  is  open  at 
the  bottom,  and  a  heavy  weight  is 
fastened  with  a  strap  to  the  piston. 
If  the  air  is  exhausted  from  the 
cylinder  above  the  piston,  the  pis- 
ton and  weight  are  raised  by  the 
upward  pressure  of  the  air  acting 
upon  the  bottom  of  the  piston. 

Figures  66  and  67  represent  two 
brass  hemispheres,  some  four  inches 
in  diameter,  the  edges  of  which  are 
made  to  fit  tightly  together.  The  whole  can  be  screwed  to  the 
air-pump  by  means  of  the  stop-cock  at  the  bottom.  While  the 
hemispheres  contain  air  they  can  be  separated  with  ease,  since 
the  outward  pressure  is  just  balanced  by  the  inward  pressure  ; 
but  when  the  air  within  is  pumped  out,  it  is  very  hard  to  pull 
them  apart.  Since  it  is  equally  difficult  to  do  this  in  whatever 
position  the  hemispheres  are  held,  the  experiment  shows  that 
the  air  presses  in  all  directions. 

This  piece  of  apparatus  is  called  the  Magdeburg  hemispheres, 
from  Otto  von  Guericke,  of  Magdeburg,  by  whom  it  was  invented. 


68 


ELEMENTS    OF 


Fig.  66. 


Fig.  67. 


The  pressure  of  the  air  at  the  level  of  the  sea  is  about 
impounds  to  a  square  inch,  or  a  ton  to  the  square  foot. 

The  surface  of  the  body 
of  a  man  of  middle  size  is 
about  1 6  square  feet ;  the 
pressure,  therefore,  which  a 
man  supports  on  the  surface 
of  his  bodyis  35,560  pounds, 
or  nearly  16  tons.  Such 
enormous  pressure  might 
seem  impossible  to  be  borne; 
but  it  must  be  remembered 
that,  in  all  directions,  there 
are  equal  and  contrary  pres- 
sures which  counterbalance 
one  another.  It  might  also 
be  supposed  that  the  effect 
of  this  force,  acting  in  all 
directions,  would  be  to  press  the  body  together 
and  crush  it.  But  the  solid  parts  of  the  skeleton 
could  resist  a  far  greater  pressure  ;  and  the  cavities  of  the  body 
are  filled  with  air  or  liquids  which  exert  a  pressure  outward 
equal  to  that  of  the  external  air.  When  the  external  pressure 
is  removed  from  any  part  of  the  body,  either  by  means  of  a 
cupping  vessel  or  by  the  air-pump,  the  pressure  from  within 
is  seen  by  the  distension  of  the  surface. 

104.  The  Pressure  of  the  Air  decreases  as  we  ascend  above 
the  Level  of  the  Sea.  —  The  pressure  of  the  air  at  the  level 
of  the  sea  is  due  to  the  downward  pressure  of  all  the  layers 
of  air  above,  transmitted  throughout  the  mass  below  ac- 
cording to  Pascal's  law  (90). 

Each  layer  of  molecules  of  air  is  pulled  downward  by  gravity, 
and  transmits  this  pressure  to  all  the  layers  below.  Hence  the 
pressure  of  a  gas  increases  with  the  depth.  It,  however,  in- 
creases more  rapidly  than  the  depth.  For,  gases  being  compres- 
sible, as  we  descend  in  a  gas  the  molecules  are  crowded  more 
closely  together,  so  that  there  are  more  molecules  exerting  pres- 


NATURAL    PHILOSOPHY. 


sure  in  each  layer,  and  there  are  more  layers  in  any  given  differ- 
ence of  depth. 

D.   LIQUIDS. 

105.  Compressibility  of  Liquids.  —  For  a  long  time  it 
was  thought  that  liquids  were  entirely  incompressible.  In 
the  year  1661  some  academicians  of 
Florence,  wishing  to  find  whether  water 
was  compressible,  filled  a  thin  globe  of 
gold  with  that  liquid,  and,  after  closing 
the  orifice  perfectly  tight,  subjected 
the  globe  to  great  pressure,  with  a 
view  of  altering  its  form,  knowing  that 
any  alteration  of  form  would  occasion  a 
diminution  of  capacity.  They  failed  to 
compress  the  water,  but  discovered 
the  porosity  of  gold,  for  the  water 
forced  its  way  through  the  pores  of  the 
globe,  and  stood  on  the  outside  like 
dew. 

In  more  recent  times  it  has  been 
shown  that  liquids  are  slightly  compres- 
sible. 

The  apparatus  for  measuring  the  compressibility  of  a  liquid 
is  shown  in  Figure  68.  It  consists  of  a  strong  glass  cylinder 
enclosing  along  glass  bulb  A,  from  which  proceeds  a  fine  bent 
tube,  with  its  end  dipping  under  the  mercury  in  the  bottom  of  the 
cylinder  at  O.  The  liquid  to  be  tested  is  introduced  into  the 
bulb  A  so  as  to  fill  both  it  and  the  tube.  The  cylinder  is  then 
filled  with  water  through  the  funnel  R,  and  pressure  applied  by 
means  of  the  thumb-screw  P.  which  forces  a  piston  down  upon 
the  water.  The  rise  of  the  mercury  in  the  fine  tube  shows  the 
amount  of  the  compression  of  the  liquid  in  the  bulb.  For  a 
pressure  of  one  atmosphere,  or  15  pounds  to  the  square  inch, 
the  volume  of  water  is  diminished  about  5  parts  in  100,000.  At 
the  depth  of  a  mile,  the  volume  of  sea-water  is  diminished  i  part 
in  130. 


70  ELEMENTS    OF 

In  liquids,  as  in  gases,  elasticity  is  developed  only  by  com- 
pression, but  their  elasticity  is  perfect.  No  matter  to  what 
pressure  a  liquid  has  been  subjected,  it  will  return  to 
exactly  its  original  volume  as  soon  as  the  pressure  is 
removed. 

1 06.  The   Tendency    of   Liquids   to  assume  a    Globular 
Form.  —  When    left  to    itself,   a  liquid   always  assumes  a 
globular  form.     This  is  because  all  the  molecules,  as  they 
work  their  way  through  the  mass,  are  stopped  by  the  force 
of  gravity  and  cohesion  at  the  same  distance  from  the  cen- 
tre of  the  mass. 

The  tendency  of  the  molecules  of  liquids  to  collect  into 
spheres -may  be  shown  by  the  following  experiment.  Prepare  a 
mixture  of  water  and  alcohol  which  shall  be  just  as  heavy  as 
sweet  oil,  bulk  for  bulk,  and  introduce  some  of  the  oil  carefully 
into  the  centre  of  this  mixture  by  means  of  a  dropping-tube  ; 
the  oil  will  neither  rise  nor  sink,  but  gather  into  a  beautiful 
sphere. 

Rain-drops,  dew-drops,  and  the  manufacture  of  shot  illustrate 
this  tendency  of  the  molecules  of  liquids.  In  the  manufacture 
of  shot,  melted  lead  is  poured  through  a  sieve  at  the  top  of  a 
very  high  tower,  and  the  drops  in  falling  take  the  form  of 
spheres,  which  become  solid  before  they  reach  the  bottom. 

107.  The  Free  Surface  of  a  Liquid  at  Rest  is  a  Level 
Surface.  —  A  level  surface  is  one  along  which  gravity  does 
not  tend  to  produce  any  motion.     Gravity  always  acts  perpen- 
dicularly to  such  a  surface,  and  hence  there  can  be  no  com- 
ponent of  gravity  which  would  tend  to  produce  motion 
along  that  surface. 

The  surface  of  a  liquid  at  rest  must  be  a  level  surface, 
else  gravity  would  tend  to  move  the  liquid  along  the  sar- 
face,  and  the  liquid  could  not  remain  at  rest. 

1 08.  The  Downward  Pressure  of  a  Liquid  due  to  Gravity 
is  proportioned  to  the  Depth.  —  Since  the  downward  pres- 
sure of  a  liquid  due  to  gravity  at  any  point  is  the  pressure 
that  has  been   transmitted   to  that  point   by   the   layers 


NATURAL    PHILOSOPHY. 


71 


of  molecules  above,  the  pressure  at  that  point  will  be 
proportional  to  the  number  of  layers  of  molecules  abore  the 
point ;  and  since  liquids  are  practically  incompressible, 
the  number  of  layers  of  molecules  will  be  proportional  to 
Ihe  depth. 

The  amount  of  pressure  transmitted  to  the  layers  below  by 
any  layer  of  molecules  is  entirely  independent  of  the  extent  of 
the  layer.  For  if  the  upper  layer  consisted  of  a  single  molecule, 
it  would  exert  the  pressure  of  a  molecule  upon  the  surface  of  a 
molecule,  and  that  pressure  would  be  transmitted  to  every  equal 
surface  below.  If  the  upper  layer  consisted  of  5  molecules,  they 
would  exert  a  pressure  of  5  molecules  upon  a  surface  of  5  mole- 
Fig.  69. 


cules,  which  would  be  the  pressure  of  one  molecule  to  the  sur- 
face of  one  molecule  as  before.  Hencr  ;he  pressure  at  any  point 
in  a  vessel  containing  a  liquid  does  Kot  depend  at  all  upon  the 
size  and  shape  of  the  vessel,  but  simply  upon  the  depth  of  the 
point  below  the  surface. 

109.  Pascal's  Vessels.  —  The  Jact  that  the  pressure  of  a 
liquid  upon  a  given  surface  depends  upon  the  depth  of  the  liquid 
only,  and  not  upon  the  size  or  shape  of  the  vessel  which  contains 
the  liquid,  may  be  illustrated  by  means  of  Pascal's  vessels 
(Figure  69).  The  vessels  M,  />,and  Q  may  in  turn  be  screwed 
into  the  plate  c.  A  disc  a  suspended  from  one  end  of  the  beam 
of  a  balance  with  a  thread,  and  held  up  by  weights  at  the  other 


72  ELEMENTS    OF 

end  of  the  beam,  serves  as  the  bottom  of  the  vessel,  which  it 
closes  water-tight.  Water  is  poured  carefully  into  the  vessel 
M  till  its  depth  is  just  sufficient  to  displace  the  plate  a,  and  the 
height  of  the  water  is  marked  by  the  point  o.  M  is  then  re- 
moved, and  P  and  Q  are  in  turn  put  into  its  place.  It  will  be 
found  that  each  will  have  to  be, filled  to  exactly  the  same  height 
to  displace  the  plate  a. 

It  follows  from  the  above  that  a  very  small  quantity  of  water 
can  produce  very  great  pressure.  Let  us  imagine  a  cask,  for 
example,  filled  with  water,  and  having  a  long  narrow  tube 
tightly  fitted  into  its  top.  If  water  is  poured  into  the  tube, 
there  will  be  a  pressure  on  the  bottom  of  the  cask  equal  to  the 
weight  of  a  column  of  water  whose  base  is  the  bottom  itself, 
and  whose  height  is  equal  to  that  of  the  water  in  the  tube.  The 
pressure  may  be  made  as  great  as  we  please ;  by  means  of  a 
mere  thread  of  water  forty  feet  high,  Pascal  succeeded  in  burst- 
ing a  very  solidly  constructed  cask. 

1 1  o.  The  Upward  Pressure  of  a  Liquid.  —  The  down- 
ward pressure  of  a  liquid  at  any  point  must  be  balanced  by 
an  equal  upward  pressure,  according  to  the  law  that  action 
and  reaction  are  always  equal  and  opposite  (30). 

The  following  experiment  (Figure   70)  serves   to  show  the 
upward  pressure  of  liquids.     A  large  open  glass  tube  A,  one 
Fig.  70.  end   of  which  is    ground,    is   fitted   with   a 

ground-glass  disc  6>,  or  still  better  with  a 
thin  card  or  piece  of  mica,  the  weight  of 
which  may  be  neglected.  To  this  is  attached 
a  string  C,  by  which  it  can  be  held  against 
the  bottom  of  the  tube.  If  the  whole  is  then 
immersed  in  water,  the  disc  does  not  fall, 
although  no  longer  held  by  the  string  ;  it 
is  consequently  kept  in  its  position  by  the 
upward  pressure  of  'the  water.  If  water  is 
now  slowly  poured  into  the  tube,  the  disc  will  sink  only  when 
the  height  of  the  water  inside  the  tube  is  equal  to  the  height 
outside. 

in.    The  Pressures  of  different  Liquids  at  the  same  Depth 


NATURAL   PHILOSOPHY.  73 

are  proportional  to  their  Densities.  —  The  pressure  at  the 
same  depth  would  be  about  12*4  times  as  great  in  mercury 
as  in  water,  and  about  .8  as  great  in  alcohol  as  in  water. 
This  is  owing  to  the  fact  that,  mercury  being  about  12^ 
times  as  dense  as  water,  each  layer  of  mercury  would 
transmit  downward  12%  times  as  much  pressure  as  a  layer 
of  the  same  thickness  of  water;  and  a  layer  of  alcohol 
.8  times  as  much. 

112.  The  Pressure  is  the  same  at  every  Point  in  a  Hori- 
zontal Layer  of  a  Liquid  at  Rest.  —  Owing  to  the  extreme 
mobility  of  liquids,  it  would  be  impossible  for  a  liquid  to 
remain  at  rest  if  at  any  point  in  it  the  pressures  acting 
upon  that  point  from   all   directions   were  not  equal    or 
balanced. 

If  the  upward  or  downward  pressure  at  any  point  were  not 
balanced,  a  particle  at  that  point  would  tend  to  move  up  or 
down  as  the  case  might  be.  If  the  pressure  were  not  the  same 
throughout  a  horizontal  layer,  there  would  be  some  point  in  the 
horizontal  layer  where  the  horizontal  pressures  to  the  right  and 
left  would  not  be  balanced,  and  a  particle  at  that  point  would 
move  in  the  direction  in  which  it  was  urged  by  the  greater 
pressure  ;  that  is,  the  liquid  would  not  be  at  rest.  This  is  true 
of  all  fluids,  both  liquids  and  gases. 

Any  disturbance  of  the  equilibrium  of  pressure  in  horizontal 
layers  gives  rise  to  currents  which  will  flow  towards  the  region 
of  low  pressure  till  the  equilibrium  is  restored. 

113.  Rise  of  Liquids  in  Communicating  Vessels.  —  When 
a  liquid  is  contained  in  vessels  which  communicate  with 
each  other  and  is  at  rest,  it  will  be  found  to  stand  at  the 
same  height  in  all  the  vessels,  whatever  may  be  their  size  or 
shape. 

Thus,  in  Figure  71,  the  water  stands  at  the  same  height  in  all 
the  tubes  as  in  the  large  vessel.  If  one  of  the  tubes  is  cut  off 
below  the  level  of  the  water  in  the  other  vessels,  and  drawn  out 
to  a  narrow  mouth,  the  liquid  will  spout  out  of  this  tube  nearly 
to  the  height  of  the  liquid  in  the  others.  The  rise  of  a  liquid 


74 


ELEMENTS   OF 


Fig.  71. 


to  the  same  height  in  a  series  of  communicating  vessels  is  due 
to  the  fact  that  when  a  liquid  is  at  rest  the  pressure  must  be 

the  same  throughout  each 
horizontal  layer.  Each 
horizontal  layer  of  the 
water  taken  through  all 
the  vessels  must  be  the 
same  distance  below  the 
free  surface  of  the  liquid 
in  each  vessel.  Hence 
these  free  surfaces  must 
be  in  the  same  horizontal 
line,  or  at  the  same  level. 

The  tendency  of  liquids 
to  find  their  own  level  is  very  important,  and  of  continual  appli- 
cation. When  any  system  of  pipes,  however  complicated,  is 
connected  with  a  reservoir,  the  water  will  rise  in  every  pipe  to 
the  level  of  the  water  in  the  reservoir. 

114.  Springs  and  Artesian  Wells. — All  natural  collections 
of  water  illustrate  the  tendency  of  a  liquid  to  find  its  level. 
Thus,  the  Great  Lakes  of  North  America  may  be  regarded  as  a 
number  of  vessels  connected  together,  and  hence  the  waters 
tend  to  maintain  the  same  level  in  all.  The  same  is  true  of  the 
source  of  a  river  and  the  sea,  the  bed  of  the  river  connecting 
the  two  like  a  pipe. 

Springs  illustrate  the  same  fact.  The  earth  is  composed  of 
layers,  or  strata,  of  two  kinds  :  those  through  which  water  can 
pass,  as  sand  and  gravel ;  and  those  through  which  it  cannot 
pass,  as  clay.  The  rain  which  falls  on  high  ground  sinks 
through  the  soil  until  it  reaches  a  layer  of  this  latter  kind,  and 
along  this  it  runs  until  it  finds  some  opening  through  which  it 
flows  as  a  spring. 

It  is  the  same  with  Artesian  wells.  These  wells  derive  their 
name  from  the  province  of  Artois  in  France,  the  first  part  of 
Europe  where  they  became  common.  It  would  seem,  however, 
that  wells  of  the  same  kind  were  made  in  China  and  Egypt, 
many  centuries  earlier. 

In  Figure  72  suppose  A  B  and  CD  to  be  two  strata  of  clay, 
and  K  J\  to  be  a  stratum  of  sand  or  gravel  between  them.  The 


NATURAL    PHILOSOPHY. 


75 


rain  falling  on  the  hills  on  either  side  will  filter  down  through 
this  sand  or  gravel,  and  collect  in  the  hollow  between  the  two 
strata  of  clay,  which  prevent  its  escape.  If  now  a  hole  is  bored 


clown  to  K K,  the  water,  striving  to  regain  its  level,  will  rise  to 
the  surface  at  H,  or  spout  out  to  a  considerable  height  above  it. 

Sometimes  the  water  between  two  such  impervious  strata 
makes  its  way  to  the  surface  through  some  fissure  in  the  upper 
stratum,  constituting  a  deep-seated  spring. 

115.  The  Spirit- Level.  —  The  spirit-level  consists  of  a  closed 
glass  tube,  A  B  (Figure  73),  with  a  slight  upward  curvature.  It 
is  filled  with  spirit,  except  Fig.  73. 

a  bubble    of  air   which      .-  —  -^^a.— — - v          ^        _^r-- j 

tends  to  rise  to  the  high-    cj     B<^  p> 

est  part  of  the  tube.     It 

is  set  in  a  case  CD,  and  when  this  is  placed  on  a  perfectly  level 

surface  the  bubble  is  exactly  in  the  middle  of  the  tube,  as  in  the 

figure. 

1 1 6.  Rise  of  two  Different  Liquids  in  Communicating  Vessels. 
—  If  into  one  of  two  communicating  tubes  (Figure  74)  we  pour 
any  liquid,  as  mercury,  it  will  rise  to  the  same  height  in  both 
branches.  If  now  we  pour  water  into  one  of  the  tubes,  the 
mercury  will  rise  somewhat  in  the  other,  but  not  nearly  so  high 
as  the  water.  The  height  of  the  two  liquids  above  the  surface 
of  separation  will  be  in  the  inverse  ratio  of  the  densities  of  the 
liquids.  This  is  because  the  pressures  of  the  two  liquids  at  the 
surface  of  separation  must  be  equal,  so  as  to  balance  each  other. 
Now  the  downward  pressure  of  the  water  at  the  surface  of  the 


76 


ELEMENTS    OF 


mercury  is   due  to  the  depth  of  the  water  above  it,  and  the 
upward  pressure  of  the  mercury  at  the  same   point  is  due  to 

the  depth  of  the  mer- 
cury above  the  level 
of  this  surface  in  the 
other  tube  ;  and  to  have 
these  pressures  equal, 
the  depths  must  be  in 
the  inverse  ratio  of  the 
densities  of  the  liquids. 
117.  Capillarity.  — 
The  rise  of  liquids  in 
communicating  ves- 
sels is  modified  in  a 
remarkable  manner 
when  any  of  the  ves- 
sels are  of  small  diam- 
eter. Such  narrow  vessels  and  fine  tubes  are  called  capillary, 
from  the  Latin  capillus,  a  hair  ;  and  their  action  upon  the 
rise  of  liquids  within  them  is  known  as  capillary  action. 

This  action  is  not,  however,  confined  to  the  cases  of  fine 
tubes ;  but  when  the  containing  vessel  is  wide,  the  action 
extends  only  a  short  distance  from  the  sides  of  the  vessel.  The 
free  surface  of  a  liquid  in  a  wide  vessel  is  not  horizontal  in  the 
neighborhood  of  the  sides  of  the  vessel,  but  presents  a  decided 
curvature.  When  the  liquid  wets  the  vessel,  as  in  the  case  of 
water  in  a  glass  vessel  (Figure  75),  the  surface  of  the  liquid 
near  the  sides  is  concave.  When  the  liquid  does  not  ivet  the 
vessel,  as  in  the  case  of  mercury  in  a  glass  vessel  (Figure  76). 
the  surface  near  the  sides  is  convex. 

When  a  narrow  tube  of  glass  is  plunged  into  water  or 
any  other  liquid  that  will  wet  it  (Figure  77),  the  liquid 
rises  higher  within  the  tube  than  on  the  outside,  and  the 
column  of  liquid  within  the  tube  will  be  concave  at  the 
top.  In  this  case  there  is  a  capillary  ascension  which 
varies  in  amount  with  the  diameter  of  the  tube  and  the 


NATURAL    PHILOSOPHY. 


77 


nature  of  the  liquid.  The  finer  the  tube,  the  higher  the 
liquid  will  rise  in  it.  If  a  glass  tube  is  plunged  in  mer- 
cury, which  does  not  wet  it,  the  mercury  \\\\\  fall  within  the 
tube  below  the  lei<el  outside  (Figure  78),  and  the  top  of  the 


Fig.  75- 


Fig.  76. 


Fig.  77. 


Fig.  78- 


column  of  mercury  within  the  tube  will  have  a  convex  sur- 
face. In  this  case  there  is  a  capillary  depression.  The 
finer  the  tube,  the  greater  the  depression. 

If  we  take  two  bent  tubes,  each  having  one  branch  of  consid- 
erable diameter,  and  the  other  extremely  narrow,  and  pour  water 
into  one  of  the  tubes,  and  mercury  into  Fig.  79. 

the  other,  the  water  will  stand  higher 
in  the  capillary  than  in  the  principal 
branch,  and  the  mercury  will  stand  lower 
in  the  capillary  branch  (Figure  79).  The 
free  surface  will  be  concave  in  both 
branches  in  the  case  of  water,  and  con- 
vex in  the  case  of  mercury.  Capillary 
action  is  manifested  whenever  the  stir- 
face  of  a  liquid  comes  in  contact  witJi  a 
solid.  If  a  clean  glass  plate  is  dipped  into  water,  the  water  will 
rise  a  little  on  each  side  of  the  plate.  If  the  same  plate  is 
dipped  into  mercury,  the  mercury  will  be  depressed  a  little  on 
each  side  of  the  plate. 

1 1 8.  Illustrations  of  Capillarity.  —  A  lamp-wick  is  full  of 
tubes  and  pores,  and  capillary  force  draws  the  oil  up  through 
these  to  the  top  of  the  wick,  where  it  is  burned.  When  one  end 
of  a  cloth  is  put  into  water,  capillary  force  draws  the  water  into 
the  tubes  and  pores  of  the  cloth,  and  the  whole  soon  becomes 
wet.  In*  the  same  way  any  other  porous  substance  soon 


7  8  ELEMENTS    OF 

becomes  wet  throughout,  if  a  corner  of  it  is  put  into  water. 
Blotting-paper  is  full  of  pores  into  which  the  capillary  force 
draws  the  ink.  The  use  of  a. towel  for  wiping  anything  which 
is  wet  depends  on  the  same  principle. 

119.  Strength  of  the   Capillary  Force. — It  is  well  known 
that  when  a  piece  of  cloth  is  wet,  it  is  almost,  if  not  quite, 
impossible  to  wring  or  squeeze  it  dry.     This   shows  that   the 
capillary  force  which  holds  the  water  in  the  pores  of  the  cloth 
is  very  strong.     Some  solids,  as  wood,  swell  on  becoming  wet. 
If  holes  are  drilled  into  a  granite  rock,  and  dry  wooden  plugs 
driven  into  them,  and  water  is  then  poured  over  the  ends  of  the 
plugs,  the  capillary  force  draws  the  water  into  the  wood,  which 
swells  and  splits  the  rock.     This  is  a  striking  illustration  of  the 
strength  of  the  capillary  force. 

1 20.  Capillary  Force  never  causes  a  Liquid  to  flow  through 
a  Tube.  —  If  a  glass  tube  is  so  fine  that  the  capillary  force  will 
draw  water  into  it  to  the  height  of  two  inches,  and  the  tube  is 
then  lowered  so  that  not  more  than  half  an  inch  shall  be  above 
the  surface  of  the  water,  the  water  will  not  overflow  the  tube. 
If,  however,  the  water  is  removed  as  soon  as  it  comes  to  the 
top,  more  will  rise  in' the  tube  to  take  its  place. 

When  a  lamp  is  burning,  the  oil  is  passing  up  continually 
through  the  wick,  because  it  is  burned  as  soon  as  it  reaches  the 
top ;  but  when  the  lamp  is  not  burning,  the  oil  does  not  overflow 
the  wick.  „ 

Fig.  80.  Fig.  81. 


121.  Heavy  Bodies  floating  on  Water  by  Capillary  Action.  — 
According  to  the  principle  of  Archimedes  (92),  a  body  cannot 
float  on  a  liquid  unless  it  is  less  dense  than  the  liquid.  This 
seems  to  be  contradicted  by  certain  well-known  facts.  Small 
steel  needles  will  float  on  water  when  placed  carefully  on  the 
surface  (Figure  80).  Some  insects  walk  on  water  (Figure  81), 


NATURAL    PHILOSOPHY.  79 

and  many  heavy  bodies  can,  if  sufficiently  minute,  float  on  the 
surface  of  water.  In  all  these  cases  the  bodies  are  not  wet  by 
the  liquid,  and  consequently  depressions 
are  formed  around  them  by  capillary  action, 
as  shown  in  Figure  82.  The  liquid  dis- 
placed by  one  of  these  bodies  is  really 
equal  to  that  which  would  fill  the  whole 
depression,  or  the  space  below  the  dotted 
line  CD  (Figure  82),  and  this  liquid  would 
in  every  case  be  equal  to  the  weight  of  the  floating  body. 

122.  Rise  of  Liquids  in  Exhausted  Tubes.  —  Since  the 
atmosphere  presses  15  pounds  to  the  square  inch  upon  the 
surface  of  a  liquid,  if  this  pressure  is  removed  or  lessened 
at  any  point  on  the  surface,  the  liquid  will  tend  to  rise  at 
that  point.  If  a  long  glass  tube,  open  at  both  ends,  is 
connected  at  the  top  by  means  of  a  rubber  tube  with  an 
air-pump,  and  is  held  upright  with  its  lower  end  under  the 
surface  of  mercury,  when  the  pump  is  worked  the  mercury 
will  begin  to  rise  in  the  tube,  and  it  will  rise  higher  and 
higher  as  the  exhaustion  continues.  If  the  air  could  be  en- 
tirely exhausted,  the  mercury  would  rise  about  30  inches 
in  the  tube.  Under  similar  circumstances  water  would  rise 
about  33  feet  high.  In  each  case  the  liquid  would  rise  in 
the  tube  till  the  pressure  within  the  tube  at  a  level  with 
the  surface  of  the  liquid  outside  was  equal  to  the  pressure 
of  the  air  on  the  surface  of  the  liquid,  or  about  15  pounds 
to  the  square  inch.  The  height  to  which  different  liquids 
will  rise  in  exhausted  tubes  will  be  in  the  inverse  ratio  oj 
the  densities  of  the  liquids. 

In  drinking  lemonade  through  a  straw,  the  air  is  first  drawr 
out  of  the  straw  by  the  mouth,  and  the  liquid  is  forced  up  through 
the  straw  by  the  pressure  of  the  air  on  the  surface.  When 
a  jar  is  filled  with  a  liquid  and  then  inverted  with  its  mouth 
under  the  same  liquid  in  a  vessel,  the  pressure  of  the  air  on  the 
surface  of^  the  liquid  in  the  vessel  will  keep  the  liquid  up  in 
the  jar. 


8o 


ELEMENTS    OF 


That  it  is  the  pressure  of  the  atmosphere  on  the  surface  of 
the  liquid  in  the  vessel  that  keeps  the  liquid  up  in  the  jar  may 
be  shown  by  the  following  experiment.  Fill  a  jar  with  mercury, 
invert  it,  and  place  its  mouth  under  some  mercury  in  a  dish. 
Place  the  jar  thus  inverted  in  the  dish  of  mercury  under  the 
receiver  of  an  air-pump,  and  exhaust  the  air.  As  the  exhaus- 
tion proceeds,  and  the  pressure  of  the  air  upon  the  surface  of 
the  mercury  becomes  less  and  less,  the  mercury  falls  in  the 
jar. 

123.  The  Fountain  in  Vacuo. — This  apparatus  is  an  illus- 
tration of  the  tendency  of  liquids  to  rise  in  exhausted  vessels 

Fig.  83. 


(Figure  83).  It  consists  of  a  bell-jar,  provided  with  a  tube  and 
stopcock  at  the  bottom.  The  bell-jar  is  first  exhausted  by 
means  of  the  air-pump.  The  stopcock  is  then  closed,  and  the 
bell-jar  is  removed  to  a  vessel  of  water.  After  the  end  of  the 
tube  has  been  placed  underwater  the  stopcock  is  again  opened. 
The  pressure  of  the  air  on  the  surface  of  the  water  in  the  vessel 
»  drives  the  water  up  in  the  bell-jar  in  a  jet  so  as  to  form  a  beauti- 
ful fountain. 

124.   Torriccltfs  Experiment.  —  Torricelli    took  a  glass 
tube  somewhat  more  than  30  inches  long  and  closed  at 


NATURAL    PHILOSOPHY. 


8l 


one  end,  and  filled  it  with  mercury.  He  then  closed  the 
tube  with  his  thumb,  and  inverted  it  in  a  dish  of  mercury 
(Figure  84).  On  opening  the  tube  under  the  mercury, 
he  found  that  the  mercury 
fell  in  the  tube  till  the  top 
of  the  column  A  stood  about 
30  inches  above  the  surface 
of  the  mercury  in  the  dish.i 
Such  a  tube  is  called  a  Tor- 
ricellian tube,  and  the  space 
above  the  column  of  mer- 
cury in  the  tube  is  called  a 
Torricellian  vacuum. 

125.  Pas caC s    Experiment. 
—  Pascal  had  .?   Torricellian 
tube  taken  from  the  bottom 
to   the    top    of    a    mountain, 
and  found    that    the    column 
of   mercury  in  the   tube  fell 
as    the     ascent     progressed. 
He  therefore  concluded  that 
the  mercury  was  kept  up  in 
the  tube  by  the  pressure  of 
the   atmosphere    on    the    sur- 
face   of  the    mercury    in    the 

vessel,     since     the     pressure 

would  necessarily  become  less  and  less  as  we  ascend  from 

the  level  of  the  sea. 

126.  The  Barometer.  —  The  barometer  is  an  instrument 
for  measuring  the  pressure  of  the  atmosphere.     It  is  a  Torri- 
cellian tube  furnished  with  a  convenient  case  (Figure  85). 
The  vessel  of  mercury  at  the  bottom  must  be  constructed 
so  as  to  prevent  the  spilling  of  the  mercury  in  transpor- 
tation, and  so  as  to  allow  the  atmosphere  to  act  freely  upon 
the  mercury. 

6 


82  ELEMENTS    OF 

F'g>  8s'  127.   Use  of  the  Barometer  in  measuring  the 

Height  of  Mountains.  —  One  of  the  chief  uses 
of  the  barometer  is  to  measure  the  height  of 
mountains.  It  has  already  been  stated  that  the 
atmospheric  pressure  is  less  as  the  height  above 
the  earth  is  greater.  When  we  have  found  at 
what  rate  it  diminishes,  we  can  readily  find  the 
height  of  mountains  by  means  of  the  barometer. 
We  have  to  find  the  difference  between  the  read- 
ings of  the  barometer  at  the  level  of  the  sea  and 
at  the  top  of  the  mountain.  This  shows  how 
much  the  pressure  has  diminished,  and  from  this 
we  can  find  the  height  of  the  mountain. 

If  the  pressure  of  the  atmosphere  decreased 
uniformly  as  we  ascend,  it  would  be  very  easy  to 
find  the  elevation  of  a  place  by  means  of  a  ba- 
rometer. But,  owing  to  the  variations  in  the 
density  of  the  air  as  we  ascend,  the  pressure 
changes  according  to  a  complicated  law  ;  and  this 
complicates  the  formula  for  finding  the  exact  ele- 
vation of  a  place  from  the  readings  of  the  barome- 
ter. As  a  rough  rule,  it  may  be  stated  that  the 
barometer  falls  one  inch  for  every  900  feet  of 
ascent. 

128.  The  Suction-Pump. — The  suction- 
pump  consists  of  a  cylinder,  or  barrel,  at  the 
top  of  a  pipe  A  (Figure  86),  communicating 
with  the  water  in  the  well  or  cistern.  A  pis- 
ton Pis  moved  up  and  down  in  the  barrel  by 
means  of  the  handle  B.  There  is  a  valve 
S  at  the  top  of  the  pipe  A,  and  another  valve  O  in  the 
piston.  Both  valves  open  upwards.  The  pump  first  ex- 
hausts the  air  from  the  pipe.  As  the  air  is  exhausted, 
the  water  is  driven  up  through  the  pipe  and  finally  into  the 
pump-barrel  by  the  pressure  of  the  air  on  the  surface  of  the 
water  in  the  cistern.  Every  time  the  piston  is  pushed 
down  the  valve  S  closes,  and  keeps  the  water  in  the  barrel 


NATURAL    PHILOSOPHY. 


from  passing  back  into  the  cistern  :  at  the  same  time  the 
valve  in  the  piston  opens,  and  allows  the  water  below  it  to 
pass  above  it.  When  the  piston  is  raised,  the  valve  O 
closes,  and  keeps  the  water  above  it  from  passing  below 
it ;  at  the  same  time  the  valve  £  is  forced  open  by  the 
pressure  from  below,  and  the  water  rushes  up  through  it 
to  fill  the  barrel  behind  the  piston.  As  the  piston  is  raised, 
the  water  above  the  piston  passes  out  by  the  discharge- 
Fig.  86.  Fig.  87. 


pipe  at  the  top  of  the  barrel.     With  this  pump  the  water 
is  raised  into  the  barrel  by  atmospheric  pressure,  and  is  then 
lifted   out  of  the  barrel    by  the  piston.      Hence  with   the 
suction-pump  water  can  be  raised  only  about  30  feet  high. 
129.    The  Force-Pump .  —  The  simple  force-pump  is  sho\ v:-, 


ELEMENTS   OF 


in  Figure  87.  The  piston  P  is  solid.  The  discharge-pipe 
D  communicates  with  the  bottom  of  the  cylinder,  and  has 
a  valve  O  in  it  opening  upward.  There  is  also  a  valve  S  in 
the  bottom  of  the  barrel,  also  opening  upward.  When  the 
plunger  is  raised  the  valve  O  closes,  and  the  water  rushes 
into  the  cylinder  through  the  valve  S;  when  the  plunger  is 
pressed  down,  the  valve  51  closes,  and  the  water  is  forced 
out  through  the  valve  O  into  the  discharge-pipe.  The 
only  limit  to  the  height  to  which  water  may  be  raised  by 
means  of  this  pump  is  that  of  the  power  used  and  of  the 
strength  of  the  pump. 

Fig.  88.  Fig.  89.  Fig.  90. 


The  force-pump  and  the  stiction-pump  may  be  combined, 
as  shown  in  Figures  88  and  89  ;  that  is  to  say,  the  cylinder  of 
the  force-pump  may  be  at  the  top  of  a  pipe  about  30  feet  above 
the  surface  of  the  water  to  be  raised. 

130.  The  Air-Chamber .  —  The  air-chamber  is  a  device 
by  which  the  water  from  a  force-pump  may  be  made  to 
escape  in  a  continuous  and  forcible  stream.  It  consists 
of  an  air-tight  box  C  above  the  valve  O  in  the  discharge- 
pipe  (Figures  87  and  90).  The  pipe  D  passes  nearly 
to  the  bottom  of  the  chamber.  When  the  pump  is  working, 


NATURAL    PHILOSOPHY. 


the  water  is  forced  into  the  air-chamber  through  the  valve 
O.  As  soon  as  the  end  of  the  pipe  D  is  covered,  the  air 
in  the  upper  part  of  the  chamber  begins  to  be  compressed. 
The  compression  i?icreases  the  elastic  force  of  the  air,  and 
causes  it  to  press  steadily  and  powerfully  on  the  surface 
of  the  water,  forcing  the  liquid  out  through  the  pipe  D  in  a 
steady  stream.  If  D  ends  in  a  narrow  nozzle,  the  water 
will  be  obliged  to  pass  through  it  very  rapidly  to  escape 
from  the  chamber  as  rapidly  as  it  is  pumped  into  it.  In 
this  way  a  stream  may  be  obtained  of  sufficient  force  to 
be  thrown  a  great  distance,  as  in  the  fire-engine. 

131.  The  Siphon. — The  siphon  is  used  for  transferring 
liquids  from  one  vessel  to  another.  It  consists  of  a  bent 
tube  with  arms  of  unequal  length  (Figure  91).  The 
air  must  be  removed  from  the  tube  in  the  first  place, 
either  by  applying  the  mouth  to  the  end  B,  after  the  other 
arm  of  the  siphon  has  been  introduced  into  the  vessel  of 
water,  or  by  filling  the  siphon  with  water  before  it  is 
placed  in  the  vessel.  The  water  will  flow  through  the 
siphon  from  C  to  B  until  Fig.  9i. 

the  vessel  is  emptied,  or 
until  the  level  of  the  water 
falls  below  the  mouth  of  the 
arm  in  the  vessel. 

The  flow  of  the  liquid 
through  the  siphon  seems  op- 
posed to  the  well-known  fact 
that  water  will  not  run  up  hill. 
But  notwithstanding  this  seem- 
ing inconsistency,  it  will  be 
seen  that  the  water  is  flowing 
from  a  higher  level  C  to  a 
lower  level  B.  If  we  consider 
a  layer  of  water  in  the  siphon 
at  J/,  we  see  that  the  force  which  acts  upon  it  from  left  to  right 
is  equal  to  the  pressure  of  the  atmosphere  minus  the  pressure  of 


86  ELEMENTS   OF 

the  water  in  the  tube  from  M  to  C,  whose  depth  is  D  C;  and 
the  pressure  which  acts  upon  it  from  right  to  left  is  equal  to  the 
pressure  of  the  atmosphere  minus  the  pressure  of  the  water  in 
the  tube  from  M  to  B,  whose  depth  is  A  B.  Since  A  £  is 
greater  than  D  C,  the  pressure  at  M  towards  the  right  will  be 
greater  than  that  towards  the  left.  Consequently  the  water  at 
M  moves  on  towards  B,  and  as  it  moves  away  more  water  is 
driven  up  into  the  arm  C  M  to  take  its  place  by  the  pressure  of 
the  atmosphere  on  the  surface  of  the  water  in  the  vessel.  No 
liquid  will  flow  through  a  siphon  unless  the  atmospheric  pressure 
is  sufficient  to  raise  it  to  the  bend  of  the  tube. 

132.  Tantalus's  Cup.  —  This  is  a  glass  cup,  with  a  siphon 
tube  passing  through  the  bottom,  as  shown  in  Figure  92.     If 
water  is  poured  into  the  cup,  it  will  rise  both  inside  and  outside 
the  siphon  until  it  has  reached  the  top  of  the  tube,  when  it  will 
begin  to  flow  out.     If  the  water  runs  into  the  cup  less  rapidly 

Fig.  92.  than  the  siphon  carries  it  out,  it  will 

sink  in  the  cup  until  the  shorter  arm 
no  longer  dips  into  the  liquid,  and 
the  flow  from  the  siphon  ceases. 
The  cup  will  then  fill,  as  before  ;  and 
so  on. 

In  many  places  there  are  springs 
which  flow  at  intervals,  like  the 
siphon  in  this  experiment,  and  whose 
action  may  be  explained  in  the  same 
way.  A  cavity  under  ground  (Fig- 
ure 93)  may  be  gradually  filled  with  water  by  springs,  and  then 
emptied  through  an  opening  which  forms  a  natural  siphon.  In 
some  cases  of  this  kind  the  flow  stops  and  begins  again  several 
times  in  an  hour. 

133.  Water- Wheels.  —  One  of  the  most  important  sources 
of  mechanical  power  is  that  of  falling  water.     The  falling 
or  running  water  is  made  to  turn  a  wheel  called  a  water- 
wheel ;  and  this  wheel,  by  means  of  bands  or  gearing,  is 
made  to  work  almost  any  kind  of  machinery. 

Water-wheels  are  of  various  forms.     Some  turn  on  an 
upright  axis,  and  others  on  a  horizontal  axis.     The  latter 


NATURAL    PHILOSOPHY. 


are  called  vertical  water-wheels,  and  the  former  horizontal 
water-wheels. 


-  93- 


One  of  the  most  common  of  vertical  water-wheels  is  rep- 
resented in  Figure  94.  It  consists  of  a  series  of  boxes, 
or  buckets,  arranged  on  Fig.  94. 

the  outside  of  a  wheel  or 
cylinder.  Water  is  al- 
lowed to  flow  into  these 
buckets  on  one  side  of  the 
wheel,  and  by  its  weight 
causes  the  wheel  to  turn. 
The  buckets  are  so  con- 
structed that  they  hold 
water  as  long  as  possi- 
ble while  they  are  going 
clown,  but  allow  it  all  to 
run  out  before  they  begin  to  rise  on  the  other  side. 

A  wheel  like  this  is  called  a  breast-wheel. 

The  overshot  wheel  is  similar  to  the  breast-wheel  in  all 
respects,  except  that  the  water  is  led  over  the  top  of  the 
wheel,  and  poured  into  the  buckets  on  the  other  side. 


88  ELEMENTS    OF 

The  tmdershot  wheel  has  boards  projecting  from  its  cir- 
cumference, like  the  paddle-wheel  of  a  steamboat.  The 
water  runs  under  the  wheel,  and  turns  it  by  the  force  of 
the  current  pressing  against  the  boards. 

134.   The  Hydraulic   Tourniquet.  —  If  a  vessel  (Figure  95), 
having  a   spout  and  faucet   on  one  side,  is  filled  with  water 
Fj  and  floated  in  a  dish  on  water  so  as  to 

move  easily,  and  the  faucet  is  then 
opened  so  as  to  allow  the  water  to 
escape,  the  vessel  will  begin  to  move 
backward.  This  is  due  to  the  reaction 
of  the  water  against  the  back  of  the  ves- 
sel. While  the  faucet  was  closed,  the 
pressure  of  the  water  against  the  front 
of  the  vessel  at  the  orifice  balanced  the 
pressure  of  the  water  against  the  back  of 
9  the  vessel  at  the  same  point.  But  when 
the  faucet  is  open,  there  is  no  pressure 

against  the  front  of  the  vessel  to  balance  the  reaction  of  the  wa- 
ter against  the  back ;  hence  the  backward  motion  of  the  vessel 
while  the  water  is  escaping. 

The  hydraulic  tourniquet  (Figure  96)  consists  of  a  vessel 

Fig.  96. 


NATURAL    PHILOSOPHY. 


89 


capable  of  turning  on  a  vertical  axis.  Two  tubes  project  from 
the  bottom  of  the  vessel  in  opposite  directions.  The  ends  of 
these  tubes  are  open,  and  are  bent  round  in  opposite  directions. 
As  the  water  escapes  from  these  tubes,  its  reaction  against  the 
parts  of  the  tubes  opposite  the  openings  causes  the  apparatus  to 
rotate  rapidly. 

135.  Turbine  Wheel.  —  One  form  of  the  turbine  -wheel  is 
shown  in  Figure  97.  This  wheel  turns  in  a  horizontal  plane. 
The  buckets  are  placed  in  the  outer  part  of  the  wheel,  which  is 
free  to  turn  on  a  vertical  axis.  The  curved  partitions,  or 
guides,  within  the  wheel  are  stationary.  These  partitions  are 
placed  at  the  bottom  of  a  long  cylinder,  into  which  the  water  is 
admitted  by  the  pipe.  The  partitions  are  curved,  so  as  to  direct 
the  water  against  the  buckets  at  the  most  advantageous  angle. 
The  water  is  discharged  at  the  rim  of  the  wheel.  Figure  98  is 
a  section  of  a  turbine  wheel.  The  buckets  are  represented  in 
the  outer  portion,  and  the  guides  in  the  inner  circle. 

There  are  many  kinds  of  turbines,  and  their  effective  power 


Fig.  97. 


Fig.  98. 


is  from  75  to  88  per  cent  of  that  in 
the  acting  body  of  water.  In  the 
best  form  of  overshot  and  breast 
wheels,  it  is  from  65  to  75  per  cent, 
and  in  undershot  wheels  from  25  to 
33  per  cent. 


ELEMENTS    OF 


D.   SOLIDS. 

136.  Tendency  of  Solids  to  assume  a  Crystalline  Struc- 
ttire.  —  Solids,  as  a  rule,  tend  to  assume  a  crystalline  struc- 
ture. "  This  tendency  is  best  shown  by  allowing  a  substance 
to  pass  gradually  from  a  liquid  to  a  solid  state. 

Place  a  rather  dilute  solution  of  acetate  of  lead  (sugar  of  lead) 
in  a  tank  with  parallel  sides  of  glass  (such  as  is  often  used  for 
projection),  and  fix  two  platinum  wires  in  the  solution,  about  an 
inch  apart.  Place  the*  tank  before  the  condenser  of  a  magic 
lantern,  and  focus  the  wires  on  the  screen.  Connect  the  wires 
with  the  poles  of  a  small  voltaic  battery.  The  lead  will  separate 
from  the  solution,  and  collect  as  a  solid  upon  the  wire  connected 
with  the  negative  pole  of  the  battery.  Beautiful  fern-like  forms 
will  be  seen  to  grow  up  on  the  screen.  These  forms  are  the 
crystals  of  lead.  As  the  substance  passes  slowly  from  the 
liquid  to  the  solid  state,  the  molecules  are  free  to  arrange  them- 
selves according  to  their  tendencies. 

If  alum  is  added  to  hot  water  as  long  as  it  will  dissolve,  and 
then  the  water  is  allowed  to  cool  slowly,  a  part  of  the  alum  will 
be  deposited  on  the  bottom  of  the  dish,  —  not  in  a  confused  mass, 
but  in  beautiful  crystals.  If  saltpetre,  nitrate  of  baryta,  or  cor- 
rosive sublimate  is  treated  in  the  same  way,  beautiful  crystals 
will  be  formed,  but  in  each  case  the  crystals  will  have  a  different 
shape. 

Melt  some  sulphur  in  a  crucible,  and  allow  it  to  cool  slowly 
Fig.  99.  till  a  crust  forms  on  the  surface  ;  then 

carefully  break  the  crust  and  pour  off 
the  remaining  liquid,  and  the  crucible 
will  be  found  lined  with  delicate  needle- 
shaped  crystals  (Figure  99). 

Large  crystals  of  many  solids  can 
be  obtained  by  dissolving  as  much  of 
the  solid  as  is  possible  in  cold  water, 

and  then  setting  it  away  in  a  shallow 

dish  where  it  will  'be  free  from  dust  and  disturbance,  and 
allowing  the  water  to  evaporate  very  slowly.     The  more 


NATURAL    PHILOSOPHY.  91 

gradual  the  formation,  the  larger  arc  the  crystals.  The  larger 
crystals  seen  in  cabinets  of  minerals  were  probably  cen- 
turies in  forming.  The  water  in  which  the  solid  was  dis- 
solved found  its  way  into  a  cavity  of  a  rock,  and  there 
slowly  evaporated. 

The  tendency  of  the  cohesive  force  to  form  the  molecules  into 
crystals  is  strikingly  shown  in  cannon  which  have  been  many 
times  fired,  and  in  shafts  of  machinery  and  axles  of  car-wheels 
which  are  continually  jarred.  Such  bodies  often  become  brit- 
tle, and  on  breaking  show  the  smooth  faces  of  the  crystals 
which  have  been  formed.  The  continued  jarring  gives  the  mole- 
cules a  slight  freedom  of  motion,  and  crystals  are  slowly  built 
up. 

Many  solids  are  crystalline  in  structure  which  do  not  appear 
to  be  so.  Thus,  a  piece  of  ice  is  a  mass  of  the  most  perfect 
crystals,  but  they  are  so  closely  packed  together  that  we  cannot 
readily  distinguish  them. 

137.  Properties  of  So/ids. —  A  body  is  said  to  be  tena- 
cious when  it  is  difficult  to  pull  it  in  two.  All  solids  are 
more  or  less  tenacious,  but  they  differ  greatly  in  the  degree 
of  their  tenacity.  A  body  is  said  to  be  hard  when  it  is 
difficult  to  scratch  or  indent  it,  that  is  to  say,  when  it  is 
difficult  to  displace  its  molecules.  All  solids  are  elastic 
within  certain  limits,  and  this  elasticity  may  be  developed 
by  stretching,  by  bending,  by  twisting,  and  by  compres- 
sion, that  is,  by  any  kind  of  strain  whatever.  Different 
solids,  however,  differ  greatly  in  the  limit  of  their  elas- 
ticity (9).  When  the  strain  is  carried  beyond  the  limit  of 
elasticity,  the  body  must  either  break  or  take  up  perma- 
nently a  new  form.  A  body  which  is  apt  to  break  when 
strained  beyond  the  limit  of  elasticity  is  said  to  be  brittle. 
A  brittle  substance  is  not  always  easily  broken.  Such  a 
body  will  not  break  unless  strained  beyond  the  limit  of  its 
elasticity,  and  that  is  often  a  difficult  thing  to  do.  It  is 
not  easy  to*  break  a  glass  rod  an  inch  in  diameter,  yet  glass 


92  ELEMENTS    OF 

is  the  most  brittle  substance  known.  Substances  which 
can  readily  take  permanently  new  forms  are  said  to  be  mal- 
leable or  ductile.  A  malleable  substance  is  one  that  can  be 
hammered  or  rolled  into  sheets,  and  a  ductile  substance  one 
that  can  be  drawn  into  wire.  All  malleable  substances 
are  to  some  extent  ductile,  but  the  most  malleable  are  not 
the  most  ductile. 

Gold  is  one  of  the  most  malleable  of  the  metals.  In  the  manu- 
facture of  gold-leaf,  it  is  hammered  out  into  sheets  so  thin  that  it 
takes  from  300,000  to  350,000  of  them  to  make  the  thickness  of 
a  single  inch. 

The  gold  is  first  rolled  out  into  sheets  by  passing  it  many 
times  between  steel  rollers  in  what  is  called  a  rolling-machine. 
The  rollers  are  so  arranged  that  they  can  be  brought  nearer  to 
each  other,  pressing  the  gold  into  a  thinner  and  thinner  sheet 
every  time  it  is  passed  between  them.  After  it  has  thus  been 
rolled  out  to  the.  thickness  of  writing-paper,  it  is  cut  up  into 
pieces  about  an  inch  square.  These  are  piled  into  a  stack  with 
alternate  pieces  of  tough  paper,  and  beaten  with  wooden  mal- 
lets. They  are  again  cut  up  into  small  pieces,  and  arranged  in 
a  stack  with  alternate  squares  of  gold-heater's  skin,  and  again 
beaten  with  mallets.  This  last  process  is  usually  repeated  three 
times. 


NATURAL   PHILOSOPHY. 


93 


II. 

SOUND. 
A.   ORIGIN  OF  SOUND. 

138.  Sound  originates  in  Molar  Vibrations.  —  Fix  a 
point  on  a  stand  so  as  to  be  nearly  in  contact  with  a  glass 
bell  (Figure  100),  and  also  hang  a  pith  ball  in  contact 

Fi"    100. 


with  the  bell  on  the  opposite  side.  If  we  draw  a  rosined 
bow  across  the  edge  of  the  bell,  this  will  be  made  to  emit 
a  musical  sound,  and  will  also  be  heard  to  tap  against 
the  point,  showing  that  it  is  in  vibration.  The  pith  ball 
will  also  be  kept  swinging  as  long  as  the  sound  continues. 
On  touching  the  bell  lightly,  we  feel  that  it  is  vibrating. 


94 


ELEMENTS    OF 


Fig.  101. 


By  grasping  it  firmly,  we  stop  both  the  vibration  and  the 
sound. 

Strike  one  prong  of  a  tuning-fork,  and  hold  it  to  the 
ear  ;  it  is  found  to  be  emitting  sound.  Fill  a  glass  brimful 
of  water,  and  hold  the  edge  of  the  prongs  in  contact  with 
the  water  ;  a  shower  of  spray  will  fly  off  on  each  side, 
showing  that  the  prong  is  in  vibration. 

When  a  string  or  wire  is  emitting  a  sound,  it  may  often 

be  seen  to  be  vibrating.     It  as-         Fig.  102 

sumes  the  form  of  an  elongated 

spindle  (Figure  101). 

If  the  front  of  an  organ  pipe 

is  made  of  glass,  and  a  little 

stretched    membrane    covered 

with   sand    is    lowered  into  it 

(Figure  102),  when  the  pipe  is 

emitting  a  sound,  the  sand  will 

be  seen  to  be  agitated,  showing 

that  the  air  within  the  pipe  is 

in  a  state  of  vibration. 

By  similar  experiments  it  has 
been  ascertained  that  every  body  which  is 
emitting  sound  is  in  a  state  of  molar  vibra- 
tion. When  the  vibration  stops,  the  sound 
ceases.  The  more  intense  the  vibration,  the 
louder  the  sound.  Sound,  therefore,  origi- 
nates i?i  molar  vibrations  of  ordinary  matter, 
solid,  liquid,  or  gaseous. 

139.  Fundamental  and  Harmonic  Vibra- 
tions. —  Strew  sand  upon  a  horizontal  plate 
of  brass,  and  then,  holding  it  with  the 
thumb  and  finger  (Figure  103),  draw  a 
bow  across  the  edge  of  the  plate  so  as  to 
throw  it  into  vibration.  The  sand  will  be  tossed  up  and 
clown  at  first,  but  will  quickly  come  to  rest  in  definite 


NATURAL    PHILOSOPHY. 


95 


lines,  called   nodal  lines.     These    are  lines  of  rest  which 
separate  the  vibrating  segments  of  the  plate.     By  touching 


the  plates  at  different  points  with  the  thumb  and  fingers, 
a  great  variety  of  figures  may  be  produced  with  the  sand, 

Fig.  194- 


96  ELEMENTS    OF 

showing  that  it  is  possible  for  the  plate  to  break  up  into 
vibrating  segments  in  a  great  many  different  ways.  A 
series  of  these  nodal  figures  is  shown  in  Figure  104. 

Strings  and  columns  of  air  may  be  also  made  to  vibrate  in 
segments.  Figure  105  shows  a  string  vibrating  as  a  whole,  in 
two  segments,  in  three  segments,  and  in  four  segments. 

The  vibration  of  a  body  as  a  whole  is  called  ^fundamental 
vibration  ;  and  the  vibration  of  its  segments,  its  harmonic  vibra- 
tion. The  harmonic  vibrations  are  more  rapid  than  the  funda- 

Fig.  105. 


mental  vibrations.  In  a  complete  series  of  harmonic  vibrations, 
the  rate  of  vibration  in  the  first  harmonic  is  twice  the  funda- 
mental rate  ;  in  the  second  harmonic,  three  times  the  fundamen- 
tal rate  ;  in  the  third  harmonic,  four  times  the  fundamental  rate; 
and  so  on. 

It  is  not  only  possible  to  produce  harmonic  vibrations  in  a 
body,  but  it  is  almost  impossible  not  to  produce  them  when 
a  body  is  thrown  into  vibration.  Whenever  the  fundamental 
vibration  of  a  body  is  started,  some  of  the  harmonic  vibrations 
are  almost  certain  to  be  started  with  it.  Hence  it  follows  that 
the  molar  vibrations  of  bodies  which  originate  sound  are  more 
or  less  complicated. 

B.    PROPAGATION  OF  SOUND. 

140.  Sound  is  not  propagated  in  a  Vacuum. — In  Figure 
1 06  the  bell  B  is  suspended  by  silk  threads  under  the 
receiver  of  the  air-pump.  The  bell  is  struck  by  means  of 


NATURAL    PHILOSOPHY. 


97 


clock-work,  which  can  be  set  in  motion  by  the  sliding-rod 

r.     If  the  bell  is  struck  before  exhausting  the  air,  it  can 

be  distinctly  heard  ;  but  as  the  air  is  exhausted,  the  sound 

becomes   fainter    and    fainter,  Fig.  106. 

until  at  last  it  can  hardly  be 

perceived,  even    with    the  ear 

close  to  the  receiver.     Sound, 

then,   cannot  pass    through    a 

vacuum. 

The  slight  sound  which  is 
heard  is  transmitted  by  the 
little  air  left  in  the  receiver, 
and  by  the  cords  which  hold 
up  the  bell. 

141.  Sound  is  propagated  in 
Gases,  Liquids,  and  Solids. — 
If  hydrogen  or  any  other  gas 
is    now  allowed    to   pass  into 
the   receiver,  the  sound  of  the 
bell  is  heard  again.     If  a  bell 
is  put  under  water  and  struck, 
it  can  be  heard.     If  a  person 
puts  his  ear  close  to  the  rail 

of  an  iron  fence,  and  the  rail  is  struck  at  a  considerable 
distance,  he  hears  the  blow  twice.  The  first  sound  comes 
through  the  rail ;  the  second,  which  soon  follows,  comes 
through  the  air.  These  experiments  show  that  sound  passes 
through  gases,  liquids,  and  solids.  Sounds  are  propagated 
chiefly  by  the  air. 

142.  Sound  is  propagated  by  Waves. —  When  any  vibrat- 
ing body,  as  the  prong  of  a  tuning-fork,  is  moving  forward, 
it  crowds  together  the  molecules  of  the  air  in  front  of  it, 
and  so  produces  a  strain  of  compression  in  the  air.     As  the 
body  moves  back  again  to  its  original  position  and  beyond 
it   on  the  other  side,  it  allows  the  molecules  of  the  air 

7 


98  ELEMENTS    OF 

behind  it  to  separate  somewhat,  and  so  produces  a  strain 
of  rarefaction  in  the  air.  Each  of  these  strains  is  propa- 
gated through  the  air  from  molecule  to  molecule  in  pre- 
cisely the  same  way  that  the  strain  of  compression  was 
propagated  from  ball  to  ball  in  Figure  8.  The  molecules 
of  air  in  front  of  the  vibrating  body  simply  vibrate  to  and 
fro  with  the  sounding  body.  This  vibrating  motion  is  also 
propagated  from  molecule  to  molecule  through  the  air ; 
but  while  the  strains  of  compression  and  rarefaction  are 
continually  moving  forward,  each  molecule  of  air  moves 
forward  a  short  distance  and  then  returns. 

The  strains  of  compression  and  rarefaction  constitute  what 
is  called  a  sound -wave,  and  each  strain  is  called  a  phase  of 
the  wave.  If  the  body  continues  in  vibration,  the  phases 
of  the  waves  will  follow  each  other  in  regular  succession. 

The  distance  occupied  by  the  two  strains  or  phases  is  called 
the  length  of  the  wave. 

As  the  strain  of  compression  is  formed  while  the  vibrating 
surface  is  moving  forward,  and  the  strain  of  rarefaction  while 
the  surface  is  moving  backward,  the  length  of  each  of  these 
phases  will  be  the  distance  the  strain  propagates  itself  while  the 
sounding  body  performs  half  a  vibration,  and  the  length  of 
the  sound-wave  will  be  the  distance  the  strain  can  propagate 
itself  while  the  sounding  body  is  making  a  complete  vibration. 
Hence,  the  faster  the  sounding  body  vibrates  the  shorter  the 
sound-waves,  and  the  slower  it  vibrates  the  longer  the  waves. 

143.  The  Intensity  of  Sound.  —  The  intensity  of  sound  at 
any  point  depends  upon  the  energy  of  the  vibration  of  the 
molecules  at  that  point. 

As  the  sound-waves  spread  in  all  directiens  from  the 
sounding  body,  a  greater  and  greater  number  of  particles 
of  air  must  be  set  in  motion,  and  the  motion  of  each  must 
be  more  feeble ;  and  since  the  surfaces  of  spheres  increase 
as  the  squares  of  their  radii,  the  number  of  particles  to  be 
set  in  motion  increases  as  the  square  of  the  distance  from 


NATURAL    PHILOSOPHY.  99 

the  sounding  body.     Sound,  then,  diminishes  in  intensity  as 
the  square  of  the  distance  from  the  sounding  body  increases. 

If  the  sound-waves  are  prevented  from  spreading  in  all  direc- 
tions, the  particles  of  air  lose  little  of  their  motion,  and  the 
sound  little  of  its  intensity.  Thus,  Biot  found  that  through  one 
of  the  water-pipes  of  Paris  words  spoken  in  a  very  low  tone 
could  be  heard  at  the  distance  of  about  three  quarters  of  a  mile. 
The  sides  of  the  pipe  kept  the  sound-waves  from  spreading.  In 
the  same  way  conversation  can  be  carried  on  between  distant 
parts  of  a  large  building  by  means  of  small  tubes,  called  speaking- 
tubes. 

144.  The  Velocity  of  Sound.  —  The  velocity  of  sound  in 
air  has  been  several  times  determined  by  experiment.     In 
1822  the  French  Board  of  Longitude  chose  two   heights 
near  Paris,  and  from  the  top  of   each  fired  a  cannon  at 
intervals  of  ten  minutes  during  the  night.     The  time  be- 
tween seeing  the  flash  and  hearing  the  report  was  care- 
fully noted  at  both  stations,  and  the  average  of  the  results 
showed  that  sound  travels  through  the  air  at  the  rate  of  1090 
feet  a  second.     In  such  experiments  the  time  taken  by  the 
light  to  pass  between  the  stations  is  too  small  to  be  per- 
ceived. 

The  velocity  of  sound  in  air  depends  somewhat  upon  the 
state  of  the  atmosphere.  Sound-waves  travel  faster  with  the 
wind  than  against  it,  and  the  higher  the  temperature  of  the  air, 
the  greater  the  velocity  of  sound  in  it.  'The  velocity  given 
above  is  for  the  temperature  of  32°. 

The  velocity  of  sound  in  water  is  about  4700  feet  a  second, 
and  its  velocity  in  solids  is  still  greater. 

145.  The  Reflection  of  Sound.  —  When  sound-waves  meet 
the  surface  of  a  new  medium,  they  are,  in  part,  thrown 
back,   or  reflected.     In  this  reflection,   as  in  all  cases  of 
reflected  motion,  the  angles  of  incidence  and  reflection 
are  equal  to  each  other. 

Echoes  are  produced  by  the  reflection  of  sound.  In  order  to 
get  an  echo,  we  must  have  a  reflecting  surface  far  enough  away 


100  ELEMENTS   OF 

to  give  an  appreciable  interval  between  the  direct  and  reflected 
sounds.  When  the  surface  is  less  than  100  feet  distant,  the 
reflected  sound  blends  with  the  direct  sound. 

The  reflecting  surface  has  often  such  a  shape  as  to  cause  the 
different  portions  of  the  reflected  wave  to  converge  to  a  point, 
and  so  to  intensify  the  reflected  sound. 

Multiple  echoes  may  be  produced  by  successive  reflections 
from  surfaces  at  different  distances  on  the  same  side,  or  by 
alternate  reflections  from  two  surfaces  on  opposite  sides.  In 
some  localities  a  pistol-shot  is  repeated  thirty  or  forty  times. 

146.  The  Speaking-Trumpet.  —  The  speaking-trumpet 
(Figure  107)  consists  of  a  long  tube  (sometimes  six  feet 
long),  slightly  tapering  towards  the  speaker,  furnished  at 
this  end  with  a  hollow  mouth-piece,  which  nearly  fits  the 
lips,  and  at  the  other  with  a  funnel-shaped  enlargement, 

Fig.  107. 


called  the  bell,  opening  out  to  a  width  of  about  a  foot. 
It  is  much  used  at  sea,  and  is  found  very  effectual  in 
making  the  voice  heard  at  a  distance.  The  explanation 
usually  given  of  its  action  is,  that  the  slightly  conical  form 
of  the  long  tube  produces  a  series  of  reflections  in  directions 
more  and  more  nearly  parallel  to  the  axis ;  but  this  explana- 
tion fails  to  account  for  the  utility  of  the  bell,  which  expe- 
rience has  shown  to  be  considerable. 

147.  The  Ear-Trumpet.  —  The  ear-trumpet  is  used  by 
persons  who  are  hard  of  hearing.  It  is  essentially  an 
inverted  speaking-trumpet,  and  consists  of  a  conical  metallic 
tube,  one  of  whose  extremities,  terminating  in  a  bell,  re- 
ceives the  sound,  while  the  other  end  is  introduced  into 
the  ear.  This  instrument  is  the  reverse  of  the  speaking- 
trumpet.  The  bell  serves  as  a  mouth-piece ;  that  is,  it 
receives  the  sound  coming  from  the  mouth  of  the  person 


NATURAL    PHILOSOPHY.  IOI 

who  speaks.  These  sounds  are  transmitted  by  a  series  of 
reflections  to  the  interior  of  the  trumpet,  so  that  the  waves, 
which  would  become  greatly  developed,  are  concentrated  on 
the  auditory  apparatus,  and  produce  a  far  greater  effect 
than  divergent  waves  would  have  done. 

148.  Loud  ness  of  Sound.  —  The  loudness,  or  intensity,  of 
sound  depends  upon  the  energy  of  the  molecular  vibrations 
in  the  sound-waves.     In  a  curve  representing  the  form  of 
the  sound-wave,  the  loud  ness  would  be  represented  by  the 
height  of  the  curve,  or  the  amplitude  of  the  wave. 

149.  Pitch  of  Sound.  —  The  pitch  of  sound  depends  upon 
the  rate  at  which  the  pulsations  of  sound  strike  upon  the 
drum  of  the  ear,  or  upon  the  length  of  the  sound-waves. 
The  length  of  the  sound-waves  depends  chiefly  upon  the 
rate  of  vibration  of  the  sonorous  body. 

Two  sounds  are  said  to  be  in  unison  when  the  rate  of 
vibration  is  the  same;  to  form  an  octave,  when  their  rates 
of  vibration  are  as  2  to  i  ;  a  fifth,  when  their  rates  of  vibra- 
tion are  as  3  to  2  ;  a  fourth,  when  their  rates  of  vibration 
are  as  4  to  3  ;  and  a  major  third,  when  their  rates  of  vibra- 
tion are  as  5  to  4. 

In  the  lowest  note  of  the  organ  there  are  16^  vibrations  a 
second.  In  the  lowest  note  of  the  piano  there  are  33  vibrations 
a  second,  and  in  the  highest  note  4224 :  giving  a  range  of 
7  octaves.  In  the  highest  note  ever  heard  in  an  orchestra  there 
are  4752  vibrations  a  second.  This  note  is  given  by  the  piccolo 
flute.  In  the  shrillest  sounds  that  are  audible  there  are  about 
32.000  vibrations  a  second,  the  upper  limit  of  audibility  varying 
with  different  persons.  The  voice  of  ordinary  chorus-singers 
ranges  from  TOO  to  1000  vibrations  a  second,  and  the  extreme 
limits  of  the  human  voice  are  50  and  1500  vibrations  a  second. 

150.  Quality  of  Sound. —  The  quality  of  sound  depends 
upon  the  form  of  the  sound-waves,  that  is,  upon  the  har- 
monic vibrations  which  are  present  with  the  fundamental 
vibrations  in  the  sonorous  body.     The  pitch  of  sound  is 


102  ELEMENTS    OF 

determined  chiefly  by  the  fundamental  note.  Two  sounds 
of  the  same  pitch  may  differ  in  quality,  because  of  differ- 
ences in  their  harmonics,  fundamental  tones  are  those 
produced  by  the  fundamental  vibrations  of  a  sonorous 
body  ;  and  harmonic  tones,  those  produced  by  the  harmonic 
vibrations.  No  two  instruments  or  voices  give  tones  of 
the  same  quality,  though  they  may  be  of  the  same  loud- 
ness  and  pitch. 

The  difference  between  a  noise  and  a  musical  sound  is  that 
the  latter  is  smooth  and  regular,  and  the  former  rough  and  irreg- 
ular. Musical  sounds  are  produced  by  rapid  periodic  vibrations 
of  a  body,  and  noises  by  non-periodic  vibrations. 

151.  Interference  of  Sound. — When  two  equal  water- 
waves  meet  in  the  same  phase,  namely,  so  that  the  crest  of 
one  coincides  with  the  crest  of  the  other,  and  the  hollow 
of  one  with  the  hollow  of  the  other,  their  combination 
produces  at  the  point  of  meeting  a  wave  of  double  the 
height.  Were  the  two  waves  to  meet  in  opposite  phases, 
that  is,  so  that  the  hollow  of  one  coincides  with  the  crest 
of  the  other,  their  combination  would  leave  the  surface  of 
the  water  undisturbed ;  there  would  be  neither  depression 
nor  elevation. 

In  a  similar  way,  when  two  equal  sound-waves  meet  in 
the  same  phase,  their  combination  would  produce  at  the 
point  of  meeting  a  wave  of  twice  the  degree  of  condensation 
and  rarefaction  of  either  of  the  component  waves.  Were 
the  two  waves  to  meet  in  opposite  phases,  the  air  would  be 
undisturbed  at  the  place  of  meeting;  there  would  be 
neither  condensation  nor  rarefaction.  An  ear  at  the  point 
of  meeting  of  the  wave  in  the  first  case  would  hear  a  sound 
much  louder  than  that  conveyed  by  either  sound-wave 
alone  ;  while  in  the  second  case  it  would  hear  no  sound  at 
all.  The  meeting  of  two  sound-waves  so  as  to  neutralize  each 
other  is  called  the  interference  of  sound. 

Strike  a  tuning-fork  so  as  to  throw  its  prongs  into  vibration, 


NATURAL   PHILOSOPHY.  103 

hold   it  vertically  near  the  ear,  and  turn  it  slowly  around  so 

as  to  bring  the  sides,  the  edges,  and  the  corners  of  the  prongs 

successively  towards  the  ear.     Four  positions  of  the  fork  will 

be  found  in  which  its  sound  will  be  in-  Fig.  108. 

audible.     Let  a  and  b  (Figure  108)  be    \ 

the  ends  of  the  prongs  of  a  tuning-fork        \ 

in  vibration.     The  sound  of  the  fork  is 

inaudible  when  the  ear  is  on  any  one  of  \ 

the  dotted  lines.    As  the  prongs  vibrate, 

each  develops  a  series  of  waves,  and 

along  the  dotted  lines  these  two  sets  of 

waves  will  be  of  equal  intensity  and  in 

opposite   phases.      Hence  along  these 

lines  the  two  sets  of  waves  neutralize  each  other,  and  silence 

results  from  the  combination  of  two  sounds. 

152.  Musical  Beats. — Suppose  two  tuning-forks,  slightly 
different  in  pitch,  to  be  started  together,  and  suppose  the 
prongs  of  both  to  be  moving  forward  at  the  same  time  ;  they 
will  start  waves  of  the  same  phase  which  will  coincide  with  and 
intensify  each  other.  The  fork  having  the  higher  pitch  will, 
however,  immediately  begin  to  gain  on  the  other,  and  the  coin- 
cidence of  the  waves  will  be  less  and  less  perfect  until  this  fork 
has  gained  half  a  vibration  on  the  other.  The  prongs  of  the 
two  forks  will  now  be  moving  in  opposite  directions  at  the  same 
time,  and  the  waves  started  by  the  two  forks  will  be  in  opposi- 
tion, and  will  neutralize  each  other  wholly  or  in  part.  After 
this  there  will  again  be  partial  coincidence  of  the  waves,  and 
the  degree  of  coincidence  will  increase  till  the  higher  fork  has 
gained  a  whole  vibration  on  the  lower  one,  when  the  coincidence 
will  again  be  complete.  When  two  such  forks  are  started 
together,  the  sound  gradually  dies  away  till  it  becomes  nearly 
-or  altogether  inaudible  ;  it  then  swells  out  loudly,  and  gradually 
dies  away  again  at  regular  intervals.  These  gradual  risings 
and  fallings  in  the  intensity  of  sound  are  called  beats. 

These  beats  occur  whenever  two  sounds  of  nearly  the  same 
pitch  are  produced  together.  The  rate  of  beating  will  be  equal 
to  the  difference  of  the  rate  of  "vibration  in  the  two  sonorous 
bodies.  If  one  of  the  bodies  gains  one  vibration  a  second  on 
the  other," the  sounds  will  beat  once  a  second;  if  it  gains  two 


104  ELEMENTS   OF 

vibrations  a  second,  the  sounds  will  beat  twice  a  second  ;  and 
so  on. 

Even  after  the  beats  become  too  rapid  to  be  distinguished 
by  the  ear,  they  give  a  disagreeable  roughness  to  the  sound. 
According  to  Helmholtz,  dissonance  is  entirely  due  to  the  rough- 
ness produced  by  a  rapid  succession  of  beats,  which  take  place 
between  either  the  fundamental  tones  or  the  harmonics  which 
are  present  in  the  two  sounds. 

C.    RESONANCE. 

153.  Sympathetic  Vibrations  of  Tuning-Porks.  —  Take 
two  tuning-forks  of  exactly  the  same  pitch,  cause  one  of 
them  to  vibrate,  and  hold  it  near  the  other  without  touch- 
ing it.  The  second  fork  will  soon  begin  to  vibrate,  and 
will  emit  a  distinctly  audible  sound  after  the  first  has  been 
stopped.  The  second  fork  will  not  be  started  by  the  first 
unless  the  two  are  of  exactly  the  same  pitch,  as  may  be 
shown  by  sticking  a  little  pellet  of  wax  to  the  prong  of  one 
of  the  forks  so  as  to  diminish  its  rate  of  vibration.  Vibra- 
tions started  in  one  body  by  the  vibrations  of  another  are 
called  sympathetic  vibrations.  The  production  of  sound  by 
sympathetic  vibrations  is  called  resonance. 

The  vibrations  are  communicated  from  one  fork  to  the  other 
by  means  of  the  air.  The  vibrations  of  the  first  fork  produce 
condensations  and  rarefactions  in  the  air  which  succeed  each 
other  at  the  rate  at  which  the  fork  is  vibrating.  The  number  of 
condensations  which  would  pass  any  point  in  a  second  is  exactly 
equal  to  the  number  of  vibrations  executed  by  the  fork  in  a 
second.  In  the  condensations  the  pressure  of  the  air  is  in- 
creased, and  in  the  rarefactions  it  is  diminished.  Each  con- 
densation as  it  passes  the  prong  of  the  second  fork  gives  it  a 
little  push.  As  the  second  fork  vibrates  at  exactly  the  same 
rate  as  the  first,  each  condensation  arrives  in  time  to  push  the 
prong  just  as  it  is  ready  to  move  forward  of  itself;  hence  the 
prong  is  always  pushed  in  the  direction  in  which  it  is  moving. 
The  push  of  one  condensation  moves  the  prong  but  little,  but 


NATURAL    PHILOSOPHY.  105 

the  pushes  are  so  timed  that  each  moves  it  a  little  farther  than 
the  last,  until  the  fork  is  made  to  vibrate  strongly. 

When  the  second  fork  cannot  vibrate  at  the  same  rate  as  the 
first,  the  condensation  will  sometimes  push  in  the  direction  in 
which  the  prong  is  moving  and  sometimes  in  the  opposite 
direction.  Hence  one  push  will  neutralize  the  effect  of  another 
instead  of  augmenting  it. 

154.  Sympathetic  Vibrations  of  Strings.  —  If  a  piano  is 
opened  and  one  of  the  keys  gently  depressed  so  as  to  raise  the 
damper  without  striking  the  string  with  the  hammer,  and  the 
note  of  the  string  is  then  sung  over  the  piano,  the  string  will 
begin  to  vibrate  and  will  emit  an  audible  sound  for  a  little  time 
after  the  voice  ceases.  It  is  only  necessary  to  hit  the  pitch  of  a 
string  accurately  and  to  sustain  the  note  sufficiently.  Strings 
may  be  thrown  into  vibration  by  their  harmonic  notes  as  well 
as  by  their  fundamental  notes. 

155.  Sympathetic  Vibrations  of  Masses  of  A  ir.  —  I  f  a  vi  brat- 
ing  tuning-fork  is  held  at  the  end  of  a  tube  an  inch  and  a  half 
or  two  inches  in  diameter,  the* sound  of  the  fork  will  be  power- 
fully reinforced,  provided  the  tube  is  of  suitable  length.     The 
suitable  length  for  a  tube  open  at  both  ends  is  one  half  of  the 
length  of  the  wave  produced  by  the  fork.     A  tube  closed  at  one 
end  resounds  most  powerfully  when  its  length  is  one  quarter  of 
the  length  of  the  wave  produced  by  the  fork.     The  column  of 
air  in  the  tube  is  thrown  into  powerful  sympathetic  vibrations 
by  the  fork,  and  these  vibrations  greatly  augment  the  sound. 
The  moment  the  fork  is  stopped  the  resonance  ceases. 

Columns  of  air  may  also  be  thrown  into  sympathetic  vibration 
by  their  harmonic  vibrations.  By  altering  the  shape  of  the  tube 
it  may  be  made  to  reinforce  certain  harmonics  more  powerfully 
than  others,  and  so  change  the  quality  of  the  exciting  sound. 

156.  Sounding  Boards  and  Boxes.  —  The  sound  of   a 
tuning-fork  is  feeble  unless  reinforced  by  a  resonant  case 
of  suitable  dimensions  to  which  the  fork  is  fixed.     Such  a 
resonant  case  is  called  a  sounding-box. 

Thin  pieces  of  dry  straight-grained  pine,  such  as  are  em- 
ployed for  the  faces  of  violins  and  the  sounding-boards  of 
pianos,  are  capable  of  vibrating  more  or  less  freely,  in  any 


106  ELEMENTS    OF 

period  lying  between  certain  wide  limits.  They  are  accordingly 
set  in  vibration  by  all  the  notes  of  their  respective  instruments  ; 
and  by  the  large  surface  with  which  they  act  upon  the  air,  they 
contribute  in  a  very  high  degree  to  increase  the  sonorous  effect. 
All  stringed  instruments  are  provided  with  sounding-boards  ; 
and  their  quality  mainly  depends  on  the  greater  or  less  readi- 
ness with  which  these  respond  to  the  vibrations  of  the  strings. 

D.    MUSICAL  INSTRUMENTS. 

157.  .Stringed  Instruments.  —  In  one  class  of  musical 
instruments  the  notes  are  produced  by  the  transverse  vibra- 
tions of  strings.  These  instruments  are  called  stringed 
instruments.  The  rate  at  which  a  string  vibrates  depends 
upon  its  length,  its  weight,  and  its  tension.  The  shorter, 

Fig.  109. 


the  tighter,  and  the  lighter  a  string,  the  faster  it  vibrates. 
Strings  may  be  thrown  into  transverse  vibration  by  draw- 
ing a  rosined  bow  across  them,  as  in  the  case  of  the  violin  ; 
or  by  plucking  them  with  the  finger,  as  in  the  case  of  the 
harp  ;  or  by  striking  them  with  a  hammer,  as  in  the  case 
of  the  piano. 

In  the  piano  there  is  a  string  for  every  note.  In  the  violin 
and  similar  instruments,  several  notes  are  obtained  from  the 
same  string  by  fingering  it  so  as  to  change  its  length  and 
tension. 

158.  The  Sonometer.  — The  sonometer  (Figure  109)  is  an 
instrument  for  investigating  the  laws  of  the  vibration  of 
strings.  It  consists  essentially  of  a  string  or  wire  stretched 
over  a  sounding-box  by  means  of  a  weight.  One  end  of 


NATURAL    PHILOSOPHY.  107 

the  string  is  secured  to  a  fixed  point  at  one  end  of  the 
sounding-box ;  the  other  end  passes  over  a  pulley,  and 
carries  weights  which  can  be  altered  at  pleasure.  Near  the 
two  ends  of  the  box  are  two  fixed  bridges,  over  which  the 
cord  passes.  There  is  also  a  movable  bridge,  which  can  be 
employed  for  altering  the  length  of  the  vibrating  portion. 

159.  Wind  Instruments.  —  In  wind  instruments  the 
notes  are  produced  by  the  longitudinal  vibrations  of  columns 
of  air  enclosed  in  pipes.  The  rate  of  vibration  depends 
upon  the  length  of  the  column,  and  upon  whether  the  pipe  is 
opened  or  closed.  The  shorter  a  column  of  air  \hefaster  it 
vibrates,  and  the  air  in  an  open  tube  vibrates  twice  as  fast 
as  that  in  a  closed  pipe  of  the  same  length.  This  is 
because  the  air  in  a  closed  pipe  vibrates  as  a  whole,  while 
that  in  an  open  pipe  vibrates  in  two  segments,  there  being 
a  stationary  point  or  node  at  the  centre  of  the  pipe. 

In  an  organ  there  are  as  many  pipes  as  notes,  only  one  note 
being  obtained  from  each  pipe.  In  the  case  of  the  flute  and 
similar  wind  instruments,  several  notes  are  obtained  from  one 
pipe  by  opening  and  closing  the  holes  at  the  side  of  the  pipe  so 
as  to  alter  the  length  of  the  vibrating  column  of  air.  and  by 
altering  the  strength  of  the  blast  so  as  to  change  from  the  fun- 
damental note  of  the  pipe  to  one  or  other  of  its  harmonics. 

In  all  wind  instruments  the  pipe  is  made  to  speak  by  reso- 
nance. The  sympathetic  vibrations  in  the  pipe  are  sometimes 
started  by  the  vibrations  of  the  lips,  as  in  the  case  of  the 
trumpet  ;  or  by  the  vibrations  of  a  spring  called  a  reed,  as  in  the 
case  of  the  clarionet ;  or  by  the  flutter  of  a  jet  of  air  when 
blown  against  a  sharp  edge,  as  in  the  case  of  the  flute. 

1 60.  Organ  Pipes.  —  Organ  pipes  are  made  of  wood  or 
metal,  and  they  are  made  to  sound  either  by  blowing  against  a 
sharp  edge  so  as  to  produce  a  flutter,  or  by  blowing  against  a 
spring  so  as  to  throw  it  into  vibration.  Pipes  which  are  made 
to  sound  in  the  first  way  are  called  flue-pipes ;  and  those  made 
to  sound  in  the  second  way,  reed-pipes.  Pipes  closed  at  one  end 
are  called  shopped  pipes  ;  and  those  open  at  both  ends  are  called 
open  pipes. 


io8 


ELEMENTS    OF 


Two  forms  of  flue-pipes  are  shown  in  Figures  no  and  in  ; 
the  one  being  made  of  wood,  the  other  of  metal.  The  air  passes 
from  the  bellows  through  the  tube  P  into  a  chamber,  which  is 
closed  at  the  top  except  the  narrow  slit  z.  The  air  compressed 
in  the  chamber  passes  through  this  slit  in  a  thin  sheet,  which 
breaks  against  a  sharp  edge  #,  and  there  produces  a  flutter. 
The  space  between  the  edge  a  and  the  slit  below  is  called  the 
mouth  of  the  pipe.  The  metal  reed  commonly  used  in  organ 


Fig.  no. 


Fig.  in. 


pipes  is  shown  in  Figures  112  and  113.  It  consists  of  a  long 
strip  of  flexible  metal  V  V,  placed  in  a  rectangular  opening, 
through  which  the  current  of  air  enters  the  pipe.  As  soon  as 
the  air  begins  to  enter  the  pipe,  the  force  of  the  blast  bends 
down  the  spring  of  the  reed  so  as  to  close  the  opening.  The 
elasticity  of  the  reed  causes  it  to  fly  back  at  once,  so  as  to  open 
the  pipe  and  allow  the  air  to  enter  again.  It  thus  breaks  up  the 
current  of  air  into  a  regular  succession  of  little  puffs. 


NATURAL    PHILOSOPHY. 


I09 


161.  The  Organ  of  the  Human  Voice.  —  The  organ  of  voice  in 
man  is  situated  at  the  top  of  the  windpipe,  or  trachea,  which  is  the 
tube  through  which  the  air  is  blown  from  the  lungs.  A  pair  of 

Figs. 


113 


Fig. 


elastic  bands,  called  the  vocal  chords,  stretched  across  the  top  of 
the  windpipe  so  as  nearly  to  close  it,  form  a  double  reed.  When 
air  is  forced  from  the  lungs  through  the  slit  between  the  chords, 
these  are  made  to  vibrate.  By  changes  in  their  tension,  their  rate 
of  vibration  is  varied,  and  the  sound  raised  or  lowered  in  pitch. 
The  cavity  of  the  mouth  and  nose  acts  as  a  resonant  tube*  and 
by  altering  the  shape  of  this  cav- 
ity we  can  give  greater  promi- 
nence to  either  the  fundamental 
note  of  the  vocal  chords  or  to 
any  of  their  harmonics. 

162.  Singing  Flames.  —  The 
air  in  an  open  tube  may  be  made 
to  give  a  sound  by  means  of  a 
luminous  jet  of  hydrogen,  coal 
gas,  etc.  When  a  glass  tube 
about  twelve  inches  long  is  held 
over  a  lighted  jet  of  hydrogen 
(Figure  114),  a  note  is  produced 
which,  if  the  tube  is  in  a  cer- 
tain position,  is  the  fundamental 
note  of  the  tube.  The  current 
of  air  passing  up  through  the 
tube  over  the  flame  causes  the  flame  to  flutter,  and  the  air  in  the 
tube  reinforces  some  pulsations  of  this  flutter  by  sympathetic 
vibration..-  The  vibration  of  the  column  of  air  in  the  tube  re- 
acts upon  the  flame,  and  causes  it  to  vibrate  more  regularly  and 


no 


ELEMENTS    OF 


more  powerfully.     The  note  depends  on  the  size  of  the  flame 
and  the  length  of  the  tube. 

If,  while  the  tube  emits  a  certain  sound,  the  voice  is  gradu- 
ally raised  to  the  same  pitch,  as  -soon  as  the  note  is  nearly 
in  unison  with  that  of  the  tube,  the  flame  is  agitated,  jump- 
ing up  and  down,  but  becomes  steady  when  the  two  sounds 
are  in  unison.  If  the  note  is  then  gradually  raised  in  pitch, 
the  pulsations  again  commence  ;  they  are  the  optical  expres- 
sions of  the  beats  which  occur  near  perfect  unison.  If,  while 
the  jet  burns  in  the  tube,  and  produces  a  note,  the  position 
of  the  tube  is  slightly  altered,  a  point  is  reached  at  which  no 
sound  is  heard.  If  now  the  voice  or  the  tuning-fork  is  pitched 
at  the  note  produced  by  the  jet,  it  begins  to  sing,  and  continues 
to  sing  even  after  the  voice  or  fork  is  silent.  A  mere  noise  or 
shouting  at  an  incorrect  pitch  affects  the  flame,  but  does  not 
cause  it  to  sing. 

Fig.  115- 


163.  Edison's  Phonograph.  —  In  Edison's  phonograph,  the 
vibrations  of  the  air  are  first  taken  up  by  a  thin  plate  of  metal, 
and  are  then  permanently  registered  on  a  sheet  of  tin-foil. 
This  instrument  (Figures  115  and  116)  consists  essentially 
of  a  brass  cylinder  C  and  of  a  mouth-piece  F.  On  the  surface 
of  the  cylinder  is  constructed  a  very  accurate  spiral  groove,  the 
threads  of  which  are  about  T^  of  an  inch  apart.  The  cylinder  is 
turned  by  the  crank  D  upon  the  axis  A  B.  On  one  end  of  this 
axis  is  cut  a  thread  of  the  same  fineness  as  the  groove  on  the 
cylinder.  A  sheet  of  tin-foil  is  fastened  smoothly  on  the  surface 
of  the  cylinder.  The  mouth-piece  (Figure  1 16)  is  supported  on 
a  post  G,  and  may  be  moved  to  and  from  the  cylinder  by  the 
lever  H.  At  the  bottom  of  the  mouth-piece  there  is  an  iron 
plate  A  about  T^T  of  an  inch  thick.  Under  this  plate  are  two 


NATURAL    PHILOSOPHY. 


II  I 


pieces  of  rubber  tubing  x  and  x,  which  separate  it  from  a  spring 
supported  by  E,  and  carrying  a  round  steel  point  P,  which  rests 
upon  the  tin-foil  on  the  cylinder,  just  over  the  spiral  groove.  If 
the  crank  is  turned,  the  thread  on  the  axis  causes  the  cylinder 
to  move  forward  so  as  to  keep  the  groove  always  under  the 
point.  When  the  iron  plate  is  at  rest,  if  we  turn  the  crank  the 
point  marks  a  spiral  line  of  uniform  depth  on  the  tin-foil.  If 
\ve  speak  or  sing  into  the  mouth-piece,  the  vibrations  of  the  air 
are  communicated  to  the  iron  plate,  and  from  this  to  the  point 

Fig.  116. 


by  means  of  the  rubber  tubing.  If  the  crank  is  turned  while 
a  person  is  speaking  or  singing  into  the  mouth-piece,  the  point 
will  mark  a  dotted  line  on  the  tin-foil.  The  depth  of  the 
indentations  will  exactly  represent  the  densities  of  the  different 
Portions  of  the  sound-waves  which  encounter  the  disc.  The 
forms  of  the  sound-waves  are  thus  registered  on  the  tin-foil,  and 
may  be  studied  at  leisure  with  the  microscope. 

If,  after  talking  into  the  mouth-piece,  we  set  the  cylinder 
back  to  the  'starting-point  and  then  turn  the  crank,  the  point 
will  follow  the  indentations  in  the  tin-foil,  and  so  be  compelled 


r 

112  ELEMENTS    OF 

to  vibrate  exactly  as  it  did  when  it  made  these  indentations  in 
the  foil.  The  vibrations  of  the  point  will  be  communicated  to 
the  thin  iron  plate  by  means  of  the  rubber,  and  by  the  plate 
to  the  air.  Thus  the  words  spoken  into  the  mouth-piece  will 
be  exactly  repeated,  and  by  the  use  of  a  properly  constructed 
mouth-piece  they  may  be  rendered  audible  throughout  a  large 
hall.  By  resetting  the  cylinder  they  may  be  repeated  several 
times,  though  more  feebly  each  time  the  foil  is  passed  under  the 
point,  the  indentations  being  gradually  smoothed  out. 

E.    THE   HUMAN    EAR. 

164.  The  Human  Ear.  —  A  section  of  the  ear  is  shown 
in  Figure  117.  The  external  opening  is  closed  at  the  bottom 
by  a  circular  membrane  called  the  tympanum,  behind  which 
is  the  cavity  called  the  drum  of  the  ear.  This  cavity  is  sep- 
arated from  the  space  between  it  and  the  brain  by  a  bony 
partition,  in  which  are  two  openings,  the  one  round  and  the 
other  oval.  These  also  are  closed  by  delicate  membranes. 
Across  the  cavity  of  the  drum  stretches  a  series  of  four  little 
bones  :  the  first,  called  the  hammer,  is  attached  to  the  tym- 
panum ;  the  second,  called  the  anvil,  is  connected  by  a  joint 
with  the  hammer  ;  a  third  little  round  bone  connects  the  anvil 
with  the  stirrup  bone,  which  has  its  oval  base  planted  against  the 
membrane  of  the  oval  opening,  almost  covering  it.  Behind  the 
bony  partition,  and  between  it  and  the  brain,  is  the  labyrinth, 
which  is  filled  with  water,  and  over  the  lining  of  which  the  fibres 
of  the  auditory  nerve  are  distributed. 

The  tympanum  intercepts  the  vibrations  of  the  air  in  the  ex- 
ternal ear,  and  transmits  them  through  the  series  of  bones  in  the 
drum  to  the  membrane  which  separates  the  drum  from  the  laby- 
rinth ;  and  thence  to  the  liquid  within  the  labyrinth  itself,  which 
in  turn  transmits  them  to  the  nerves.  The  transmission,  how- 
ever, is  not  direct.  At  a  certain  place  within  the  labyrinth,  ex- 
ceedingly fine  elastic  bristles,  terminating  in  sharp  points,  grow 
up  between  the  nerve  fibres.  These  bristles  of  Schultze  (so 
called  from  the  discoverer)  are  exactly  fitted  to  sympathize  with 
those  vibrations  of  the  water  which  correspond  to  their  proper 
periods.  Thrown  thus  into  vibration,  the  bristles  stir  the  nerve 
fibres  which  lie  between  their  roots,  and  the  nerve  transmits  the 


NATURAL    PHILOSOPHY. 


impression  to  the  brain,  and  thus  to  the  mind.  At  another  place 
in  the  labyrinth  we  have  little  crystalline  particles,  calle'd  oto- 
litks,  embedded  among  the  nervous  filaments,  and  exerting, 
when  they  vibrate,  an  intermittent  pressure  upon  the  adjacent 
nerve  fibres.  The  otoliths  appear  to  be  fitted,  by  their  weight, 
to  receive  and  prolong  the  vibrations  of  evanescent  sounds 
which  might  otherwise  escape  attention.  The  bristles  of  Schultze, 
on  the  contrary,  are  peculiarly  fitted  for  the  transmission  of  con- 
tinuous vibrations.  Finally,  there  is  in  the  labyrinth  the  organ 
of  Corti  (named  from  the  discoverer^,  which  is  to  all  appearance 

Fig.  117. 


a  musical  instrument,  with  its  chords  so  stretched  as  to  receive 
vibrations  of  different  periods,  and  transmit  them  to  the  nerve 
filaments  which  traverse  the  organ.  Within  the  ear  of  man, 
and  without  his  knowledge  or  contrivance,  this  lute  of  3000 
strings  has  existed  for  ages,  receiving  the  music  of  the  outer 
world,  and  rendering  it  fit  for  reception  by  the  brain.  Each 
musical'tremor  which  falls  upon  this  organ  selects  from  its  tense 
fibres  the  one  appropriate  to  its  own  pitch,  and  throws  that  fibre 
into  sympathetic  vibration.  And  thus,  no  matter  how  compli- 
cated the  motion  of  the  external  air  may  be,  these  microscopic 
strings  can  analyze  it,  and  reveal  the  elements  of  which  it  is 
composed.  - 


114  ELEMENTS   OF 


III. 

HEAT. 

I.    EFFECTS    OF   HEAT. 
/ 

A.    EXPANSION. 

165.  Expansion  of  Solids.  —  As  a  rule,  bodies  expand 
ivhen  heated,  solids  being  the  least  expansible,  liquids  next, 
and  gases  the  most  expansible. 

The  linear  expansion  of  a  solid  may  be  illustrated  by  means 
of  the  apparatus  shown  in  Figure  118.  The  metal  rod  A  is  sup- 
ported on  two  standards.  It  is  fastened  at  the  end  B  by  the 
binding  screw  ;  the  other  end  passes  loosely  through  its  stand- 
ard, and  presses  against  the  short  arm  of  the  index  K,  which 

Fig.  118. 


moves  over  a  graduated  arc.  Under  the  rod  there  is  a  vessel 
filled  with  alcohol.  The  rod  is  adjusted  so  that  the  index  shall 
be  at  zero  on  the  scale,  and  the  alcohol  is  lighted.  As  the  rod 
becomes  heated,  the  index  rises,  showing  that  the  rod  has  ex- 
panded in  length  so  as  to  move  forward  the  short  arm  of  the 
index. 

If  a  brass  and  iron  rod  of  the  same  length  and  thickness  are 
tried  in  succession,  and  each  is  raised  to  a  bright  red  heat,  it 


NATURAL    PHILOSOPHY.  115 

will  be  found  that  the  brass  rod  will  expand  considerably  more 
than  the  iron.  As  a  rule  different  solids  expand  unequally  when 
heated  equally. 

The  cubical  expansion  of  a  solid  may  be  illustrated  by  means 
of  the  ring  and  ball  shown  in  Figure  119.  When  cool,  the  ball 
will  just  pass  through  the  ring.  If  we  heat  the  ball  by  holding 
it  for  a  time  in  the  flame  of  the  lamp,  it  will  no  longer  pass 
through  the  ring ;  but  if  allowed  to  cool,  it  will  again  pass 
through.  If,  while  the  heated  ball  rests  on  the  ring,  this  is 
heated  equally  with  the  ball,  the  latter  will  again  pass  through 
the  ring,  the  two  being  equally  expanded  by  the  heat. 

1 66.  Force  of  Expansion  of  Solids.  —  The  force  of  ex- 
pansion is  very  great,  being  equal  to  that  which  would  be 

Fig. 


necessary  to  compress  the  body  to  its  original  dimensions. 
Thus,  for  instance,  iron  when  heated  from  32°  to  212° 
increases  by  .0012  of  its  original  length.  In  order  to 
produce  a  corresponding  change  of  length  in  a  rod  an 
inch  square,  a  force  of  about  15  tons  would  be  required. 

It  would  be  useless  to  attempt  to  offer  any  mechanical  resist- 
ance to  a  force  so  enormous  ;  the  only  thing  that  can  be  done,  in 
the  case  of  structures  in  which  metals  are  employed,  is  to  ar- 
range the  parts  in  such  a  manner  that  the  expansion  shall  not  be 
attended  with  any  evil  effects.  Thus,  in  a  railway,  the  rails  do 
not  touch  each  other,  a  small  interval  being  left  to  allow  room 
for  the  variations  of  length.  Iron  beams  employed  in  buildings 
must  have  the  ends  free  to  move  forward,  without  encountering 
any  obstacles,  which  they  would  inevitably  overthrow.  Sheets 


u6 


ELEMENTS    OF 


of  zinc  or  lead  employed  in  roofing  are  so  arranged  as  to  be  able 
to  overlap  one  another  on  expansion. 

167.  Compensating  Pendulum.  —  Suppose  a  clock  to  keep 
exact  time  at  a  certain  temperature  ;  then,  if  the  temperature 
rises,  the  length  of  the  pendulum  will  increase  (62),  and  with  it 
the  duration  of  each  oscillation,  so  that  the  clock  will  lose. 
The  opposite  effect  would  be  produced  by  a  fall  of  temperature. 
Hence  the  clock  is  liable  to  go  too  fast  in  winter,  and  too  slow  in 

Fig.  120. 


Fig.  121. 
_J 

I 

F 

f 

f 

1 

q    c 

c 
T~ 

— 

C 

summer  ;  and  we  must  move  the  ball  of  the  pendulum  from  time 
to  time  in  order  to  insure  its  regularity. 

The  effect  of  temperature  may  be  notably  diminished  by 
means  of  compensating  pendulums,  of  which  there  are  several 
different  kinds. 

Harrison's  gridiron  pendulum  (Figures  120  and  121)  consists 
of  four  oblong  frames,  the  uprights  of  which  are  alternately  of 


NATURAL    PHILOSOPHY.  llf 

brass,  C,  and  of  steel,  F.  These  are  so  put  together  that  the 
expansion  of  the  steel  rods  alone  would  tend  to  lower  the  ball, 
while  the  expansion  of  the  brass  rods  alone  would  tend  to  raise  it. 
The  lengths  of  the  rods  are  so  adjusted  that  the  expansion  of 
one  set  of  rods  shall  just  balance  that  of  the  other,  thus  keeping 
the  ball  of  the  pendulum  all  the  time  at  exactly  the  same  distance 
from  the  point  of  suspension. 

Graham's  pendulum  consists  of  an  iron  rod  carrying  at 
the  bottom  a  frame  which  holds  one  or  two  tubes  containing 
mercury  I  Figure  122).  The  mercury  takes  the  place  of  the 
ball  of  the  pendulum.  The  expansion  of  the  rod  tends  to 
lower  the  centre  of  gravity  of  the  mercury,  while  the  expansion 
of  the  mercury,  since  it  is  free  to  expand  only  upward,  tends  to 
raise  the  centre  of  gravity.  The  quantity  Fig.  123. 

of  mercury  is  adjusted  so  that  its  expan- 
sion shall  balance  that  of  the  rod,  and  thus 
keep  the  centre  of  gravity  of  the  mercury 
at  the  same  height  all  the  time. 

1 68.  Compensation  Balance-Wheel. — 
The  rate  of  a  watch  is  controlled  by  the 
vibration    of    the    balance-wheel.      The 
larger  this  wheel  the  slower  it  vibrates. 

and  the  smaller  it  is  the  faster  it  vibrates.  Hence  changes  of 
temperature  have  the  same  effect  on  the  rate  of  watches  as  on 
that  of  clocks.  The  rim  of  the  compensation  balance-wheel  (Fig- 
ure 123)  is  made  in  sections,  which  are  weighted  at  their  free 
ends,  and  are  composed  of  two  metals,  the  more  expansible  of 
which  is  on  the  outer  side  of  the  sections.  The  expansion  of  the 
spokes  tends  to  carry  the  weights  away  from  the  centre  of  the 
wheel  and  so  to  make  the  wheel  larger.  When  the  sections  of 
the  rim  expand,  they  become  more  curved,  since  they  expand 
more  rapidly  on  the  outside  than  on  the  inside  ;  hence  they 
tend  to  carry  the  weight  in  towards  the  centre  and  so  to  make 
the  wheel  smaller.  The  parts  of  the  wheel  are  so  adjusted  that 
the  expansion  of  the  sections  of  the  rim  just  balances  that  of  the 
spokes. 

169.  Expansion  of  Liquids.  —  The  expansion  of  a  liquid 
may  be  illustrated  by  means  of  a  bulb  with  a  projecting 


n8 


ELEMENTS   OF 


Fig.  124. 


tube  (Figure  124),  filled  with 
water  or  other  liquid  up  to  the 
point  a.  If  the  bulb  is  immersed 
in  a  vessel  of  hot  water,  the  liquid 
in  the  stem  at  first  falls  to  />,  and 
then  gradually  rises  to  a.  The 
liquid  falls  at  first,  because  the 
bulb,  being  the  first  heated,  is 
also  the  first  to  expand,  and  its 
capacity  is  thus  increased.  After- 
wards, as  the  liquid  becomes 
heated,  it  expands  more  rapidly 
than  the  globe ;  hence  it  rises  in 
the  tube. 

If  two  bulbs,  with  projecting 
tubes,  and  of  exactly  the  same 
size,  are  filled,  one  with  water 
and  the  other  with  alcohol,  and 
are  then  heated  equally,  the  alco- 
hol will  be  seen  to  expand  more  rapidly  than  the  water. 
In  general,  different  liquids  when  heated  equally  expand  un- 
equally. 

170.  Anomalous  Expansion  and  Contraction  of  Water. — 
If  we  fill  a  bulb  and  tube  with  water,  and  surround  the  bulb 
with  a  freezing  mixture,  the  water  in  the  stem  will  steadily  fall 
till  the  temperature  of  the  water  has  reached  39°  ;  it  will  then 
begin  to  rise  again,  and  will  continue  to  rise  till  the  temperature 
reaches  32°.    If  now  the  bulb  is  gradually  heated,  the  water  will 
fall  in  the  stem  till  the  temperature  reaches  39°  ;  it  will  then 
begin  to  expand,  and  will  continue  to  expand  until  it  boils. 
Water  at  39°  will  expand  whether  it  is  heated  or  cooled.     It 
follows  from  this,  that  water  is  at  its  greatest  density  at  39°. 
Hence  this  point  of  temperature  is  called  its  point  of  maximum 
density. 

171.  Expansion  of  Gases.  —  The  expansion  of  air  may 


NATURAL    PHILOSOPHY. 


Fig.  125. 


be  illustrated  by  means  of  the  bulb  and 
tube  shown  in  Figure  125.  The  bulb  is 
filled  with  air,  which  is  separated  from 
the  external  air  by  a  small  column  of 
liquid  in  the  stem,  which  serves  also  as 
an  index.  When  the  globe  is  warmed 
by  the  hands,  the  index  is  rapidly  pushed 
up.  It  has  been  found  that  all  gases 
expand  equally  for  the  same  rise  of  tem- 
perature, and  that  under  a  uniform  pres- 
sure a  gas  will  expand  so  as  to  double 
its  volume  for  a  rise  of  temperature  of 
about  490°. 

172.  Expansion  due  to  an   Increase  of 
Molecular  Motion.  —  The  molecules  of  bod- 
ies are  all  the  time  moving  rapidly  to  and 
fro.     When  heat  is  applied  to  a  body,  its 
molecules  are  made  to  move  more    rapidly, 

and  this  increased  agitation  causes  them  to  move  farther  apart, 
and  the  body  to  expand. 

B.  MEASUREMENT  OF  TEMPERATURE. 

173.  Temperature.  — When  we  wish  to  indicate  hoiv  hot 
a  body  is,  we  say  that  it  has  a  certain  temperature.     The 
word  temperature  is   the   noun  which  corresponds  to  the 
adjective  hot.     We  estimate  how  hot  a  body  is  from  its 
power  of  imparting  heat  to  other  bodies.     The  body  which 
has  the  greater  power  of  imparting  heat  is  said   to  be  the 
hotter,  or  to  have  the  higher  temperature. 

Temperature  is  the  thermal  condition  of  a  body  considered 
with  reference  to  its  power  of  imparting  heat  to  other  bodies. 

An  instrument  used/0/-  measuring  temperature 'is  called  a 
thermometer. 

174.  jThe  Mercurial  Thermometer. —  In    ordinary  ther- 
mometers changes  of  temperature  are  indicated  and  meas- 


I2O 


ELEMENTS   OF 


Fig.  126. 


ured  by  the  expansion  and  contraction  of  mercury. 
The  instrument  is  called  a  mercurial  thermome- 
ter. It  consists  essentially  (Figure  126)  of  a 
tube  with  a  very  fine  calibre,  closed  at  one 
end,  and  having  a  reservoir  at  the  other  end, 
usually  in  the  form  of  a  globe  or  cylinder. 
The  bulb  and  a  portion  of  the  stem  are  filled 
with  mercury.  As  the  temperature  changes, 
the  top  of  the  column  of  mercury  in  the  tube 
rises  and  falls.  A  scale  is  either  engraved  on 
the  stem  or  placed  behind  it. 

175.  How  the  Mercurial  Thermometer  is 
Graduated.  — The  two  fixed  points  of  tempera- 
ture are  those  at  which  ice  melts  and  water  boils. 
The  former  is  called  \\\e  freezing-point,  and  the 
latter  the  boiling-point. 

In  order  to  determine  the  position  of  the  freezing-point  on  the 
stem,  the  bulb  and  the  lower  part  of  the  stem  are  surrounded  by 
melting  ice,  contained  in  a  perforated 
vessel  so  as  to  allow  the  water  pro- 
duced by  the  melting  to  escape  (Figure 
127).  When  the  column  in  the  stem 
ceases  to  fall,  a  mark  is  made  on  the 
tube,  with  a  fine  diamond,  at  the  top  of 
the  mercurial  column.  This  mark  in- 
dicates the  position  of  the  freezing- 
point  for  this  particular  thermometer. 

In  order  to  obtain  the  position  of 
the  boiling-point,  the  bulb  and  stem 
of  the  thermometer  are  enveloped  in 
steam  from  boiling  water,  as  shown  in 
Figure  128.  The  height  to  which  the  mercury  rises  is  then 
marked  on  the  stem. 

176.  The  Fahrenheit  and  Centigrade  Scales.  —  There  are 
two  thermometer  scales  in  common  use,  the  Fahrenheit  and 
the  Centigrade.  The  ordinary  scale  in  use  in  this  country 


Fig.  127. 


NATURAL    PHILOSOPHY. 


121 


and  in  England  is  the  Fahrenheit  scale.  On  this  scale  the 
freezing-point  is  marked  32  and  the  boiling-point  212.  The 
space  between  the  freezing  and  boiling  points  is  divided 
into  1 80  equal  parts,  each  of  which  is  called  a  degree. 
These  divisions  are  continued  on  the  scale  above  the 
boiling-point  and  below  the  freezing-point  to  the  ends  of 

Fig.  128. 


the  tube.     A  Fahrenheit  degree  is  T|Q  of  the  difference  of 
temperature  between  the  freezing  and  boiling  points. 

On  the  Centigrade  scale  the  freezing-point  is  marked  o 
and  the  boiling-point  100,  and  the  space  between  the  two 
is  divided  into  100  equal  parts,  the  divisions  being  con- 
tinued to  the  ends  of  the  tube.  A  Centigrade  degree  is 
T£y  of  the  difference  of  temperature  between  the  freez- 


122  ELEMENTS    OF 

ing   and   boiling  points.     A   Fahrenheit  degree  is  f  of  a 
Centigrade  degree. 

The  zero  of  the  Centigrade  scale  is  the  temperature  of 
melting  ice.  The  zero  of  the  Fahrenheit  scale  is  32°  below 
the  melting-point  of  ice.  It  was  the  lowest  temperature  that 
Fahrenheit  could  obtain  with  a  mixture  of  salt  and  ice. 

177.  Alcohol  Thermometers. —  Mercury  freezes  at  a  temper- 
ature of  about  40°  below  zero,  or  of  — 40°  F.;  hence  it  cannot 
be  used  for  measuring  temperatures   below   that   point.     Low 
temperatures  are  sometimes  measured  by  means  of  an  alcohol 
thermometer.     This  is  constructed  in  the  same  way  as  a  mer- 
curial thermometer,  but  the  bulb  is  rilled  with  alcohol  instead  of 
mercury.     As  alcohol  boils  at  a  temperature  of  about  175°   F. 
an   alcohol  thermometer  cannot  be  used  for  measuring   high 
temperatures. 

178.  Pyrometers.  —  Mercury  boils  at  a  temperature  of  about 
670°  F.  ;  hence  it  cannot  be  employed  to  measure  temperatures 
above  that  point.     Very  high  temperatures  are  often  measured 
by  the  expansion  of  solids.     The  instrument  used  is  called  a 
Pyrometer.     One  form  of  pyrometer  (Figure  129)  consists  of  a 

Fig.  129. 


bar  of  iron  lying  in^the  groove  of  a  porcelain  slab.  One  end 
of  the  iron  bar  presses  against  the  end  of  the  groove,  and  the 
other  end  against  the  arm  of  an  indicator.  As  the  bar  expands 
it  moves  the  index  point,  the  position  of  which  indicates  roughly 
the  temperature  to  which  the  bar  is  exposed.  Such  pyrometers 
are  not  very  accurate.  „ 

179.  The  Differential  Thermometer.  —Leslie's  differential 
thermometer  (Figure  130)  enables  us  to  measure  small  varia- 
tions of  temperature.  A  column  of  sulphuric  acid,  colored  red, 
stands  in  the  two  branches  of  a  bent  tube,  which  terminates 
in  two  globes  of  equal  volume.  When  the  air  contained  in 


NATURAL    PHILOSOPHY. 


I23 


Fig.  130. 


the  two  globes  is  at  the  same  temperature,  the  liquid  stands 
at  the  same  height  in  the  two 
branches.  This  point  is  marked 
zero.  One  of  the  globes  being  then 
maintained  at  a  constant  tempera- 
ture, the  other  is  raised  through, 
for  instance,  5  degrees,  when  the 
column  rises  on  the  side  of  the 
colder  globe  up  to  a  point  a,  and 
descends  on  the  other  side  to  a 
point  b.  Suppose  the  space  trav- 
ersed by  the  liquid  in  each  branch 
to  be  divided  into  10  equal  parts, 
each  part  will  be  equivalent  to  a 
quarter  of  a  degree.  This  division 
is  continued  upon  each  branch  on 
both  sides  of  zero. 


QUESTIONS  ON   THERMOMETER   SCALES. 

72.  Oil  of  vitriol  freezes  at  —  30°  F.     This  is  equivalent  to 
what  temperature  on  the  Centigrade  scale  ? 

73.  Lead  melts  at  620°  F.      What  is   the   temperature   at 
which  lead  melts  on  the  Centigrade  scale  ? 

74.  Iron  melts  at  2800°  F.      What  is  the  equivalent  tempera- 
ture on  the  Centigrade  scale  ? 

75.  What  temperature  on  the  Fahrenheit  scale  corresponds 
to  50°  C.  ?     To  -  25°  C.  ?     To  380°  C.  ? 

C.   CHANGE  OF  STATE. 

/.   FUSION  AND   SOLIDIFICATION. 

1 80.  The  Fusing-Point. —  When  any  solid  is  sufficiently 
heated  it  will  melt,  but  different  solids  melt  at  very  different 
temperatures.  The  temperature  at  which  a  solid  melts  is 
called  its  melting-point  or  fusing-point.  Mercury  melts  at 
—  40°  F.,  ice  at  32°  F.,  lead  at  608°  F.,  and  silver  at  1832°  F. 

Most  substances  expand  on  melting,  but  a  few,  like  ice,  con- 
tract. When  a  substance  expands  on  melting,  an  increase  of 


124  ELEMENTS    OF 

pressure  upon  it  will  tend  to  hinder  its  melting,  and  will  there- 
fore raise  its  melting-point ;  but  if  it  contracts  on  melting,  an 
increase  of  pressure  will  tend  to  help  its  melting,  and  will 
accordingly  lower  its  melting-point. 

The  passage  from  the  solid  to  the  liquid  state  is  generally 
abrupt,  but  this  is  not  always  the  case.  Glass,  for  instance, 
before  reaching  a  state  of  perfect  liquefaction,  passes  through 
a  series  of  intermediate  stages  in  which  it  is  of  a  viscous  con- 
sistency, and  can  be  easily  drawn  out  into  exceedingly  fine 
threads,  or  moulded  into  different  shapes. 

181.  Constant  Temperature  during  Fusion.  —  During  the 
entire  time    of    fusion    the    temperature  remains    constant. 
Thus,  if  a  vessel  containing  ice  is  placed  on  the  fire,  the 
ice  will  melt  more  quickly  as  the  fire  is  hotter  ;  but  if  the 
mixture  of  ice  and  water  is  constantly  stirred,  a  thermom- 
eter placed  in  it  will  indicate  the  temperature  32°  without 
variation,  so  long  as  any  ice  remains  unmelted  ;  it  is  only 
after  all  the  ice  has  become  liquid  that  a  rise  of  tempera- 
ture will  be  observed. 

182.  Latent  Heat  of  Fusion.  —  As  we  have  just  seen,  all 
the  heat  that  enters  the  body  while  it  is  undergoing  fusion  is 
employed  in  changing  its  state.     The  heat  thus  employed  is 
said  to  be  rendered  latent,  and  is  called  the  latent  heat  of 

fusion,  or,  since  it  exists  in  the  latent  state  in  the  liquid 
formed,  the  latent  heat  of  the  liquid. 

183.  Solidification.  —  Were    any    substance    sufficiently 
cooled,  it  would  become  solid.     This  conversion  of  a  sub- 
stance into  a  solid  by  a  reduction  of  temperature  is  called 
solidification,  or  congelation. 

184.  Change  of  Volume  in  Congelation.  —  In  passing  from 
the   liquid   to   the   solid    state,   bodies  generally  undergo  a 
diminution  of  volume ;  there  are,  however,  exceptions,  such 
as  ice,  bismuth,  silver,  cast-iron,  and  type-metal.     It  is  this 
property  which   renders    these    latter   substances   so  well 
adapted  for  casting,  as  it  enables  the  metal  to  penetrate 
completely  into  every  part  of  the  mould. 


NATURAL    PHILOSOPHY.  125 

The  expansion  of  ice  is  considerable,  amounting  to  about  ^ 
of  its  bulk ;  its  production  is  attended  by  enormous  mechanical 
force,  just  as  in  the  analogous  case  of  expansion  by  heat  (166). 
Its  effect  in  bursting  water-pipes  is  well  known.  Major  Williams 
at  Quebec  filled  a  1 2-inch  shell  with  water,  and  closed  it  with  a 
wooden  plug,  driven  in  with  a  mallet.  The  shell  was  then  ex- 
posed to  the  air,  the  temperature  being  —  18°  F.  The  water 
froze,  and  the  plug  was  projected  to  a  distance  of  more  than  100 
yards,  while  a  cylinder  of  ice  of  about  8  inches  in  length  was 
protruded  from  the  hole.  In  another  experiment  the  shell  split 
in  halves,  and  a  sheet  of  ice  issued  from  the  rent  (Figure  131)- 

Fig.  131. 


It  is  the  expansion  and  consequent  lightness  of  ice  which 
enables  it  to  float  on  the  surface  of  the  >vater,  and  to  protect 
animal  life  beneath. 

//.    EVAPORATION  AND  CONDENSATION. 

185.  Evaporation  of  Liquids.  —  The  majority  of  liquids, 
when  left  to  themselves  in  contact  with  the  atmosphere, 
evaporate,  that  is,  gradually  pass  into  the  state  of  vapor  and 
disappear.  This  occurs  much  more  rapidly  with  some 
liquids  than  with  others,  and  those  which  evaporate  most 
readily  are  said  to  be  the  most  volatile.  Thus,  if  a  drop  of 
ether  is  let  fall  upon  any  substance,  it  disappears  almost 
instantaneously ;  alcohol  also  evaporates  very  quickly,  but 
water  requires  a  much  longer  time.  The  change  is  in  all 


126  ELEMENTS    OF 

cases  accelerated  by  an  increase  of  temperature;  in  fact,  when 
we  dry  a  body  before  the  fire,  we  are  simply  availing  our- 
selves of  this  property  of  heat  to  hasten  the  evaporation 
of  the  moisture  of  the  body.  Evaporation  may  also  take 
place  from  solids. 

1 86.  Gas  and  Vapor.  —  The  words  gas  and  vapor  have 
no  essential  difference  of  meaning.  A  vapor  is  the  gas 
into  which  a  liquid  is  changed  by  evaporation.  Every 
gas  is  probably  the  vapor  of  a  certain  liquid.  The  word 
vapor  is  especially  applied  to  the  gaseous  condition  of 
bodies,  which  are  usually  met  with  in  the  liquid  or  solid 
state,  as  water,  sulphur,  etc.  ;  while  the  word  gas  generally 
denotes  a  body  which,  under  ordinary  conditions,  is  never 
found  in  any  state  but  the  gaseous.  When  the  air  or  any 
other  gas  contains  all  the  vapor  it  can  hold,  it  is  said  to  be 
saturated  with  that  vapor.  The  amount  of  vapor  required 
to  saturate  a  gas  increases  with  the  temperature.  This 
may  be  shown  by  the  following  experiment.  Pour  a  few 
drops  of  water  into  a  glass  flask,  and  then  apply  heat  till 
the  water  is  entirely  evaporated  and  the  flask  appears  dry. 
If  the  flask  is  allowed  to  cool,  moisture  will  collect  on  its 
inner  surface. 

187.  Dry  Air  and  Currents  of  Air  favorable  to  Evapora- 
tion. —  The  dryer  the  air  the  more  rapid  the  evaporation,  be- 
cause the  more  readily  will  the  atmosphere  take  up  the  vapor 
formed.     Currents  of  air  favor  evaporation,  because  they  pre- 
vent any  layer  of  air  from  remaining  long  enough  in  contact  with 
the  liquid  to  become  saturated  with'  vapor.     Other  things  being 
equal,  wet  clothes  will  dry  much  faster  on  a  windy  day  than  on 
a  still  day. 

1 88.  Latent  Heat  of  Evaporation.  —  Evaporation  is  a 
cooling  process.     If  a  few  drops  of  ether  are  allowed  to  fall 
on  the  hand,  they  will  evaporate  rapidly,  and  a  sensation 
of  cold  will  be  experienced.     If  the  bulb  of  a  thermometer 
is  dipped  in  ether  and  removed,  the  ether  which  adheres 


NATURAL    PHILOSOPHY.  12? 

to  it  will  quickly  evaporate,  and  the  mercury  will  fall  sev- 
eral degrees.  The  heat  consumed  in  evaporating  a  liquid 
is  called  the  latent  heat  of  evaporation,  or  the  latent  heat  of 
the  Tapor. 

189.  Ebullition.  —  When  a  liquid  contained  in  an  ojjen 
vessel  is  subjected  to  a  continual  increase  of  temperature, 
it  is  gradually  changed  into  vapor.     This  action  is  at  first 
confined  to  the  surface  ;  but  after  a  certain  time  bubbles  of 
vapor  are  formed  in  the  interior  of  the  liquid,  which  rise 
to    the  top,   and   set   the   entire   mass  in   motion    with  a 
characteristic  noise  ;  this  is  what  is  meant  by  ebullition,  or 
boiling. 

If  we  observe  the  gradual  progress  of  this  phenomenon,  — 
for  example,  in  a  glass  vessel  containing  water,  —  we  shall  per- 
ceive that  after  a  certain  time  very  minute  bubbles  are  given 
off ;  these  are  bubbles  of  dissolved  air.  Soon  after,  at  the  bot- 
tom of  the  vessel,  larger  bubbles  of  vapor  are  formed,  which 
decrease  in  volume  as  they  ascend,  and  disappear  before  reach- 
ing the  surface.  This  stage  is  accompanied  by  a  peculiar 
sound,  and  the  liquid  is  said  to  be  singing.  The  sound  is 
probably  caused  by  the  collapsing  of  the  bubbles  as  they  are 
condensed  by  the  colder  water  through  which  they  pass. 
Finally,  the  bubbles  increase  in  number,  growing  larger  as  they 
ascend,  until  they  burst  at  the  surface,  which  is  thus  kept  in  a 
state  of  agitation ;  the  liquid  is  then  said  to  boil. 

190.  Difference  between  Evaporation  at  the  Boiling-Point 
and   below    the    Boiling- Point.  —  Below   the   boiling-point 
evaporation  takes  place  only  at  the  surface ;  the  tension,  or 
elastic  force,  of  the  vapor  is  less  than  that  of  the  atmos- 
phere ;  and  only  a  part  of  the  heat  received  by  the  liquid 
is  used  in  converting  the  liquid  into  vapor,  the  tempera- 
ture of  the  liquid  rising  all  the  time  that  heat  is  applied  to 
it.     At  the  boiling-point  evaporation  takes  place  through- 
out the  liquid  ;  the  tension  of  the  vapor  formed  is  equal  to 
that  of  the   atmosphere ;  and  all  the  heat  received  by  the 
liquid  is  used  in  converting  it  into  steam,  the  temperature 


128 


ELEMENTS    OF 


remaining  stationary.  The  elastic  force  of  the  vapor  given 
off  by  a  liquid  increases  with  the  temperature,  until  we 
reach  the  boiling-point,  when  it  equals  that  of  the  atmos- 
phere. The  boiling-point  of  a  liquid  is  therefore  the  tem- 
perature at  which  the  elasticity  of  the  vapor  is  equal  to  the 
pressure  of  the  atmosphere  on  the  surface.  It  follows  from 
this  that  the  boiling-point  must  vary  with  the  pressure. 
Under  a  pressure  less  than  that  of  the  atmosphere  the 
boiling-point  of  water  is  below  212°,  and  under  a  greater 
pressure  than  that  of  the  atmosphere  is  above  212°. 

-191.  Franklin's  Experiment.  — Boil  a  little  water  in  a  flask 
long  enough  to  expel  all  the  air  from  the  flask.     Remove  the 
Fig.  132.  flask    from    the     source     of 

heat,  cork  it  securely,  and 
invert  it  with  its  corked 
end  under  water.  Ebullition 
ceases  almost  instantly.  Pour 
cold  water  over  the  flask 
(Figure  132)  and  the  liquid 
will  begin  to  boil,  and  will 
continue  to  do  so  for  some 
time.  The  contact  of  the 
cold  water  with  the  flask 
lowers  the  temperature  and 
tension  of  the  steam  which 
presses  on  the  surface  of  the 
water,  and  the  diminution  of 
pressure  allows  the  water  to  boil  at  a  lower  temperature. 

192.  Papin^s  Digester.  —  In  a  confined  vessel  water  may  be 
raised  to  a  higher  temperature  than  in  the  open  air,  but  it  will 
not  boil.  This  is  the  case  in  the  apparatus  called,  from  its  in- 
ventor, Papiii's  digester  (Figure  133)-  It  is  a  bronze  vessel  of 
great  strength,  covered  with  a  lid  secured  by  a  powerful  screw. 
It  is  employed  for  raising  water  to  very  high  temperatures, 
and  thus  obtaining  effects  which  would  not  be  possible  with 
water  at  212°,  such,  for  example,  as  dissolving  the  gelatine  con- 
tained in  bones. 


NATURAL    PHILOSOPHY. 


129 


Fig.  133- 


The  tension  of  the  steam  increases  rapidly  -with  the  tempera- 
ture.. Thus,  at  392°  the  pressure  is  that  of  16  atmospheres,  or 
about  240  pounds  'on  the  square  inch.  In  order  to  obviate  the 
risk  of  explosion,  Papin  introduced  the  device  known  as  the 
safety-valve.  It  consists  of 
an  opening,  closed  by  a  coni- 
cal valve  or  stopper,  which  is 
kept  down  by  a  lever  loaded 
with  a  weight.  Suppose  the 
area  of  the  lower  end  of  the 
stopper  to  be  i  square  inch, 
and  that  the  pressure  is  not  to 
exceed  10  atmospheres,  cor- 
responding to  a  temperature 
of  356°.  The  magnitude  and 
position  of  the  weight  are  so 
arranged  that  the  pressure 
on  the  whole  is  10  times  15 
pounds.  If  the  tension  of 
the  steam  exceeds  10  atmos- 
pheres, the  lever  will  be  raised,  the  steam  will  escape,  and  the 
pressure -will  be  thus  relieved. 

193.  Condensation   of    Vapors.  —  Condensation,    or    the 
conversion  of  a  vapor  into  a  liquid,  is  the  reverse  of  evap- 
oration.     In    condensation,  the   heat   rendered   latent   in 
evaporation  is  again  set  free  as  sensible  heat.      As  an  in- 
crease of  temperature  and  a  diminution  of  pressure  pro- 
mote evaporation,  so  a  diminution  of  temperature  and  an 
increase  of  pressure  promote  condensation. 

194.  Distillation.  —  Distillation  consists  in  boiling  a  liquid 
and  condensing  the  vapor  evolved.     It  enables  us  to  separate 
a  liquid  from  the  solid  matter  dissolved  in  it,  and  to  effect  a 
partial  separation  of  the  more  volatile  constituents  of  a  mixture 
from  the  less  volatile.     The  apparatus  employed  is  called  a  still. 
One  of  its  simpler  forms,  suitable  for  distilling  water  (Figure 
134),  consists  of  a  retort  a,  the  neck  of  which  c  communicates 
with  a  spiral  tube  dd,  called  the  worm,  placed  in  a  vessel  e,  con- 
taining cold  water.     The  water  in  the  retort  is  boiled,  the  steam 

9 


13° 


ELEMENTS    OF 


given  off  is  condensed  in  the  worm,  and  the  distilled ivater  is  col- 
lected in  the  vessel^".  As  the  condensation  proceeds,  the  water 
of  the  cooler  becomes  heated,  and  must  be  renewed.  For  this 
purpose  a  tube  descending  to  the  bottom  of  the  cooler  is  sup- 
Fig. 


plied  with  a  continuous  stream  of  cold  water  from  above,  while 
the  warm  water,  which  rises  to  the  top,  flows  out  by  the  tube  i. 

195:  The  Spheroidal  State.  —  This  is  a  peculiar  condition 
assumed  by  liquids  when  exposed  to  the  action  of  very  hot 
metals. 

If  we  let  fall  a  drop  of  water  upon  a  smooth  plate  of  iron  or 
Fig.  135.  silver,   the   drop    will   evaporate 

more  rapidly  as  the  temperature 
of  the  plate  is  increased  up  to  a 
certain  point.  When  the  tem- 
perature exceeds  this  limit,  which, 
for  water,  appears  to  be  about 
300°,  the  drop  assumes  a  sphe- 
roidal form,  rolls  about  like  a  ball 
or  spins  on  its  axis,  and  fre- 
quently exhibits  a  beautiful  rip- 
pling (Figure  135).  While  in 
this  condition  it  evaporates  much 
more  slowly  than  when  the  plate  was  at  a  lower  temperature.  If 
the  plate  is  allowed  to  cool,  a  moment  arrives  when  the  globule 
of  water  flattens  out,  and  boils  rapidly  away  with  a  hissing  noise. 
If  the  temperature  of  the  liquid  is  measured  by  means  of  a 


NATURAL    PHILOSOPHY.  131 

thermometer  with  a  very  small  bulb,  it  is  always  found  to  be 
below  the  boiling-point. 

\  n  the  spheroidal  state  the  liquid  and  the  metal  plate  do  not  come 
into  contact.  To  prove  this,  the  plate  used  must  be  quite  smooth 
and  accurately  levelled.  When  it  is  heated,  a  little  water  is  poured 
upon  it  and  assumes  the  spheroidal  state.  By  means  of  a  fine 
platinum  wire  the  globule  is  kept  at  the  centre  of  the  plate.  It 
is  then  very  easy,  by  placing  a  light  behind  the  globule,  to  see  dis- 
tinctly the  space  between  the  liquid  and  the  plate  (Figure  136). 

This  separation  is  maintained  by  the  rush  of  steam  from  the 
under  surface  of  the  globule,  which  is  also  the  cause  of  the  pe- 

Fig.  136. 


culiar  rippling  movements.  In  consequence  of  the  separation, 
heat  can  pass  to  the  globule  only  by  radiation,  and  hence  its 
comparatively  low  temperature. 

D. .  MEASUREMENT  OF  HEAT. 

196.  The   Unit  of  Heat.  —  The  temperature  of  a  body 
indicates  its  thermal  condition,  but  not  the  amount  of  heat 
in  it.     The  thermometer  shows  a  pound  of  iron  and  ten 
pounds  of  iron  to  be  of  the  same  temperature,  when,  of 
course,  the  latter  has  ten  times  as  much  heat  in  it  as  the 
former.     In  the  measurement  of  heat  we  need  some  unit 
in  which  amounts  of  heat  can  be  expressed.     The  English 
unit  of  heat  is  the  amount  of  heat  required  to  raise  one  pound 
of  water  at  32°  one  degree  in  temperature. 

197.  Specific  Heat.  —  If  equal  bulks  of  water  and  of  mercury 
are  exposed  to  the  same  source  of  heat,  it  will  be  found  that  the 
temperature  of  the  mercury  will  rise  faster  than  that  of  the  wa- 
ter, though  the  mercury  is  more  than  12  times  as  heavy  as  the 


132  ELEMENTS    OF 

water.  It  has  been  'found  that  it  requires  very  different  amounts 
of  heat  to  raise  the  same  weight  of  different  substances  one  de- 
gree in  temperature. 

The  specific  heat  of  a  substance  is  the  amount  of  heat  re- 
quired to  raise  one  pound  of  it  one  degree  in  temperature.  The 
specific  heat  of  water  is  I,  and  it  is  higher  than  that  of  any  other 
substance,  with  the  single  exception  of  hydrogen. 

198.  A  Body  in   Cooling  \°  gives  out  just  as  much  Heat 
as  it  takes  to  Heat  it  i°.  —  Boil  a  quarter  of  a  pound  of  wa- 
ter in  a  beaker,  and  the  bulb  of  a  thermometer  plunged 
into  it  will  indicate  a  temperature  of  212°.     Remove  the 
beaker  from  the  source  of  heat,  and  pour  the  water  into 
another  beaker  containing  a  quarter  of  a  pound  of  water 
at  a  temperature  of  70°.     Stir  the   mixture  a  short  time 
with  the  bulb  of  a  delicate  thermometer,  and  the  tempera- 
ture will  be  found  to  be  141°.    The  first  quarter  of  a  pound 
of  water  has  then  lost  71°,  and  the  second  has  gained  71° ; 
in  other  words,  the  first  in  cooling  one  degree  has  given  out 
just  heat  enough  to  warm  the  second  one  degree.    The  same  is 
true  of  all  other  bodies. 

199.  The   Water  Calorimeter.  —  A  calorimeter  is  an  instru- 
ment/br  measuring  quantities  of  heal.     The  water  calorimeter 
is  a  vessel  containing  water  into  which  a  heated  substance  may 
be  introduced.     As  the  substance  cools  it  imparts  some  of  its 
heat  to  the  water,  and  the  amount  of  heat  given  up  by  the  sub- 
stance may  be  calculated  from  the  weight  of  the  water  in  the 
calorimeter  and  the  number  of  degrees  the  temperature  is  raised. 
The  number  of  units  of  heat  received  by  the  water  will  be  equal 
to  the  product  of  the  rise  of  temperature  in  degrees  and  the 
weight  of  the  water  in  pounds.     This  method  of  measuring  heat 
is  called  the  method  of  mixture. 

200.  The  Latent  Heat  of  Water.— By  the  latent  heat  of 
water  we  mean  the  amount  of  heat  required  to  melt  a  pound 
of  ice.     This  is  found  to  be  143  units. 

201.  The  Ice  Calorimeter.  —  Another  method  of  finding  spe- 
cific heat  is  by  melting  ice.     The  substance  is  first  weighed, 


NATURAL    PHILOSOPHY.  133 

then  heated  to  a  certain  temperature,  as  100°,  and  placed  in  the 
vessel  M  (Figure  137).  This  vessel  is  placed  within  the  vessel 
A,  the  space  between  the  two  being  filled  with  ice.  The  vessel 
A  is  placed  in  another,  B,  from  which  it  is  also  separated  by 
ice.  Since  the  vessel  A  is  surrounded  by  ice,  the  heat  which 
melts  the  ice  within  it  must  come  wholly  from  the  vessel  J/. 
As  the  ice  in  A  melts,  the  water  runs  off  through  the  pipe  D. 
As  we  know  how  much  heat  is  required  to  melt  one  pound  of 
ice,  we  need  only  know £010  much  ice  is  melted  by  any  substance 


Fig.  137- 


within  the  box  J/,  in  order  to  find  how  many  units  of  heat  it  has 
given  up.  Dividing  this  by  the  weight  of  the  substance  and  by 
the  number  of  degrees  it  has  cooled,  we  get  its  specific  heat. 

202.  The  Latent  Heat  of  Steam.  —  The  latent  heat  of 
watery  vapor,  or  steam,  is  higher  than  that  of  any  other 
vapor,  being  967  units. 

The  latent  heat  of  steam  may  be  found  by  allowing  a  quan- 
tity of  steam  to  pass  into  a  water  calorimeter.  The  steam  will 
be  condensed,  and  the  water  formed  will  be  cooled  to  the  re- 
sulting temperature  of  the  water  in  the  calorimeter.  The  heat 
given  out  in  this  condensation  and  cooling  will  raise  the  tem- 
perature of  the  water  in  the  calorimeter.  The  amount  of  this 
heat  may  be  calculated,  as  well  as  the  amount  of  heat  given  out 


134  ELEMENTS    OF 

in  the  cooling  of  the  water  formed  from  the  steam.  The  dif- 
ference between  these  two  amounts  will  be  the  amount  of  heat 
set  free  in  the  condensation  of  the  steam.  This,  divided  by  tlie 
•weiglit  of  the  steam,  will  give  its  latent  heat. 

II.    RELATIONS   BETWEEN    HEAT   AND   WORK. 

203.  Heat  consumed  in  the  Performance  of  Work. —  In 
expansion,    liquefaction    of    solids,  and    evaporation,    the 
molecules  are  always  pushed   into    new  positions  against 
some  kind  of  resistance,  either  internal  or  external ;  that 
is  to  say,  work  is  done  upon  the  molecules.     This  work  is 
always  done  at  the  expense  of  heat,  either  of  that  already 
in  the  body  or  of  that  communicated  to  the  body.     Hence, 
whenever  any  of  these  kinds  of  work  are  done  without  the 
application  of  heat  to  the  body,  some  of  the  heat  in  the 
body  is  consumed  and  its  temperature  falls  ,•  and  whenever 
the  work  is  done  by  the  application  of  heat,  the  temperature 
of  the  body  rises  less  than  it  would  with  the  same  application 
of  heat  were  no  work  done. 

204.  Heat  consumed  in  Expansion.  —  If  a  thermometer 
bulb  is  introduced  into  the  receiver  of  an  air-pump  through 
an  opening  into  which  it  is  fitted  air-tight  by  means  of  a 
rubber  cork,  and  the  pump   is  worked,  as  the  exhaustion 
proceeds  the   air  in  the   receiver  will  expand  more    and 
more,  and  the  mercury  in  the  stem  of  the  thermometer  will 
fall  several  degrees,  indicating  a  reduction  of  temperature. 
The  air  is  always  chilled  when  any  expansion  takes  place  in 
it  ivithoiit  the  application  of  heat. 

It  takes  6.7  units  of  heat  to  raise  the  temperature  of  a  cubic 
foot  of  air  490°  when  the  air  is  confined  so  that  it  cannot  expand, 
and  9.5  units  to  raise  the  temperature  the  same  amount  when 
the  air  is  free  to  expand.  In  the  latter  case  the  air  will  expand 
enough  to  double  its  volume  (171).  So  that  2.8  units  of  heat  are 
consumed  in  expanding  a  cubic  foot  of  air  enough  to  double  its 
volume.  The  heat  consumed  in  expansion  is  called  the  latent 
heat  of  expansion.  The  conversion  of  sensible  into  latent  heat 


NATURAL    PHILOSOPHY. 


'35 


Fig.  138. 


is  simply  the  transformation  of  kinetic  into  potential  energy. 
When  the  air  contracts  again,  the  potential  energy  is  trans- 
formed again  into  kinetic  energy,  and  the  latent  heat  again 
becomes  sensible. 

205.  Heat  consumed  in  Liquefaction.  —  Place  some  pul- 
verized nitrate  of  ammonia  in  a  small  beaker  glass,  add  an 
equal  bulk  of  water,  and  stir  the  mixture  with  the  bulb  of 
a  thermometer.     The  solid  will  be  rapidly  dissolved,  and 
the  temperature  of  the  mixture  will  quickly  fall  40  or  50 
degrees.     If   put  upon  a  wet  board,  the  beaker  will    be 
quickly  frozen  to  it.     In  the  liquefaction  of  a  solid  a  part  of 
its  kinetic  energy  is  transformed  into  potential  energy,  and 
sensible  heat  becomes  latent  heat.     In  the  solidification  of  the 
liquid  the  potential  energy  is  transformed  back  again  into 
kinetic   energy,  and  the  latent  heat  again  becomes  sensible 
heat. 

In  the  melting  of  a  solid  all 
the  kinetic  energy  that  enters  the 
body  is  transformed  into  potential 
energy  by  the  conversion  of  the 
solid  into  a  liquid,  and  hence 
there  is  no  rise  of  temperature 
while  the  solid  is  melting. 

206.  Heat  consumed  in   Evapo- 
ration. —  The  consumption  of  heat 
in   evaporation   may  be  illustrated 
by  means  of  the  cryophorus  (Fig- 
ure 138).     It  consists  of  a  bent  tube  with  a  bulb  at  each 
end.     It  is  partly  filled  with  wate^an^hermetically  sealed 
while  the  liquid  is  boiling,  thus  expelling  the  air.     When 
an  experiment  is  to  be  made,  all  the  liquid  is  passed  into 
B,  and  A  is  plunged  into  a  freezing  mixture,  or  into  pounded 
ice.     The  cold  condenses  the  vapor  in  A,  and  thus  pro- 
duces rapid  evaporation  of  the  water  in   B.     Needles  of 
ice  soon  appear  on  the  surface  of  the  liquid. 


,36 


ELEMENTS    OF 


Pour  a  little  water  into  a  small  test-tube,  and  place  the  tube 
in  a  wineglass  of  ether  (Figure  139);  then  blow  a  current  of  air 
through  the  ether  by  means  of  a  pair  of  bellows.  The  rapid 
evaporation  of  the  ether  will  reduce  the  temperature  sufficiently 
to  freeze  the  water  in  the  tube  in  a  short  time. 

In  evaporation  as  in  liquefaction,  the  conversion  of  sensible 
into  latent  heat  is  merely  the  transformation  of  kinetic  energy 
into  potential  energy. 

207.  Freezing  Mixtures.  —  The  ordinary  freezing  mixture 
is  a  mixture  of  salt  and  ice.  The  salt  causes  some  of  the 

Fig.  139 


ice  to  liquefy,  and  this  liquefaction  consumes  so  much 
heat  that  the  temperature  of  the  mixture  is  reduced  suffi- 
ciently to  freeze  cream  within  a  can  which  is  surrounded 
by  the  mixture. 

A  mixture  of  solidified  carbonic  acid  and  ether,  in  the  re- 
ceiver of  an  air-pump  from  which  the  air  has  been  exhausted  so 
as  to  promote  the  evaporation,  evaporates  with  very  great  ra- 
pidity, and  the  consumption  of  heat  is  so  great  as  to  reduce  the 
temperature  of  the  mixture  to  —  166°  F. 


NATURAL    PHILOSOPHY.  137 

A  mixture  of  solidified  nitrous  oxide  and  bisulphide  of  carbon, 
under  similar  circumstances,  evaporates  still  more  rapidly,  and 
reduces  the  temperature  to  —  220°  F. 

208.  Solidification  of  Gases.  —  If  any  gas  is  liquefied  by 
the  combined  action  of  cold  and  pressure,  and  then  allowed 
to  escape  into  the  atmosphere  in  a  fine  stream,  so  as  to 
evaporate  freely,  the  temperature  will  be  reduced  to 'such 
an  extent  that  a  portion  of  the  vapor  will  be  frozen,  so  that 
the  gas  can  be  obtained  in  a  solid  state. 

In  the  case  of  hydrogen,  and  some  other  gases,  which  cannot 
be  liquefied  by  the  direct  action  of  cold  and  pressure,  if  the  gas 

Fig.  140. 


is  reduced  to  the  greatest  possible  degree  of  density  by  the  com- 
bined action  of  cold  and  pressure,  and  then  is  allowed  to  expand 
by  a  sudden  removal  of  the  pressure,  the  sudden  expansion  chills 
the  gas  sufficiently  to  freeze  a  portion  of  it  (204).  Hydrogen 
frozen  in  this  way  is  heard  to  rattle  like  hail  when  it  falls  on  the 
table. 

Faraday  was  the  first  to  conduct  methodical  experiments  in 
the  liquefaction  of  gases.  The  apparatus  employed  by  him 
(Figure  140)  consists  of  a  very  strong  bent  glass  tube,  closed  at 
both  ends.v  One  end  of  this  contains  the  ingredients  which,  on 
the  application  of  heat,  evolve  the  gas  to  be  tried,  while  the  other 


138  ELEMENTS    OF 

is  immersed  in  a  freezing  mixture.  The  pressure  produced  by 
the  evolution  of  the  gas  in  large  quantity  in  a  confined  space 
combines  with  the  cold  of  the  freezing  mixture  to  produce  lique- 
faction of  the  gas,  and  the  liquid  collects  in  the  cold  end  of  the 
tube. 

209.  Mechanical  Equivalent  of  Heat.  —  Meyer  found    the 
equivalent  of  a  unit  of  heat  in  foot-pounds •,  by  converting  heat 
into  mechanical  energy  through  the  expansion  of  air.     In  the 
expansion  of  air  the  work  done  is  wholly  external,  namely,  that 
of  pushing  aside  the  surrounding  air.     We  have  seen  (204)  that 
it  takes  2.8  units  of  heat  to  expand  a  cubic  foot  of  air  to  double  its 
volume.  To  ascertain  the  amount  of  work  done  in  pushing  away 
the  surrounding  air,  Meyer  imagined  his  cubic  foot  of  air  at  the 
bottom  of  a  prismatic  box  whose  section  was  a  foot  square,  so 
that  the  air  could  expand  only  upward.     The  upper  surface  of 
the  cubic  foot  of  air  contains  144  square  inches.     Hence  the 
weight  of  the  column  of  air  pressing  upon  this  surface  is  about 
144  X  15  =  2160  pounds;  and  when  the  cubic  foot  of  air  ex- 
pands so  as  lo  double  its  volume,  this  weight  must  be  raised  one 
foot  high.     Hence  2.8  units  of  heat  are  equivalent  to  2160  foot- 
pounds of  mechanical  energy,  and  one  unit  of  heat  is  equivalent 
to  ni  foot-pounds.     This  is  known  as  the  mechanical  equivalent 
of  heat. 

210.  The  Steam- Engine.  —  The  molecular  energy  of  heat  can 
be  made  to  do  mechanical  work  by  means  of  the  arrangement 
shown  in  Figure  141.     The  steam  derives  its  expansive  power 
from  the  heat,  and  this  expansive  power  is  made  tp  work  a  pis- 
ton in  the  cylinder  of  the  steam-engine.     The  steam  from  the 
boiler  passes  through  the  tube  x  into  the  steam-box  d.     Two 
pipes  run  from  this  box,  one  a  to  the  top  and  the  other  b  to  the 
bottom  of  the  cylinder.      A  sliding- valve  y  is  so  arranged  as 
always  to  close  one  of  the  pipes  to  the  steam-box  and  open  it  to 
the  exit-pipe  O,  and,  at  the  same  time,  to  open  the  other  pipe  to 
the  steam-box  and  close  it  to  the  exit-pipe.     In  the  right-hand 
figure  the  lower  pipe  b  is  open,  and  the  steam  can  pass  in  under 
the  piston  and  force  it  up.     At  the  same  time  the  steam  which 
has  done  its  work  on  the  other  side  of  the  piston  passes  out 
from  the  cylinder  through  the  pipes  a  and  O. 

The  sliding- valve  is  connected  by  means  of  the  rod  /with  the 


NATURAL    PHILOSOPHY. 


'39 


crank  of  the  engine,  so  that  it  moves  up  and  down  as  the  piston 
moves  down  and  up.  As  soon,  then,  as  the  piston  has  reached 
the  top  of  the  cylinder,  the  sliding- valve  is  brought  into  the  posi- 
tion shown  in  ihe  left-hand  figure.  The  steam  now  passes  into 
the  cylinder  above  the  piston  through  the  pipe  a,  and  forces  the 

Fig-  141. 


piston  down,  and  the  steam  on  the  other  side  which  has  done  its 
work  goes  out  through  b  and  O.  The  sliding-valve  is  now  again 
in  the  position  shown  in  the  right-hand  figure,  and  the  piston  is 
driven  up  again  as  before  ;  and  thus  it  keeps  on  moving  up  and 
down,  or  in  and  out. 

III.    DISTRIBUTION   OF   HEAT. 

A.   CONDUCTION. 

211.  Illustration  of  Conduction.  —  If  heat  is  applied  to 
one  end  of  a  bar  of  metal,  it  is  slowly  propagated  through 
the  substance  of  the  bar,  producing  a  rise  of  temperature 


140  ELEMENTS    OF 

which  is  first  perceptible  near  the  heated  end,  and  after- 
wards in  more  remote  portions.  The  transmission  of  heat 
from  molecule  to  molecule  through  the  substance  of  the  body 
is  called  conduction. 

If  the  application  of  heat  to  one  end  of  the  bar  is  continued 
for  a  sufficiently  long  time,  and  with  great  steadiness,  the  differ- 
ent portions  of  the  bar  will  at  length  cease  to  rise  in  tempera- 
ture, and  will  retain  steadily  the  temperatures  which  they  have 
acquired.  We  may  thus  distinguish  two  stages  in  the  experi- 
ment :  ist,  the  variable  stage,  during  which  all  portions  of  the 
baf  are  rising  in  temperature  ;  and  2d,  the  permanent  state, 
which  may  subsist  for  any  length  of  time  without  alteration.  In 
the  former,  the  bar  is  gaining  heat  ;  that  is,  it  is  receiving  more 
heat  from  the  source  than  it  gives  out  to  surrounding  bodies. 
In  the  latter,  the  receipts  and  expenditure  of  heat  are  equal,  not 
only  for  the  bar  as  a  whole,  but  for  every  small  portion  of  it. 

In  the  permanent  state  no  further  accumulation  of  heat  takes 
place.  All  the  heat  which  reaches  an  internal  particle  is  trans- 
mitted by  conduction,  and  the  heat  which  reaches  a  superficial 
particle  is  given  off  partly  by  radiation  and  air-contact,  and 
partly  by  conduction  to  colder  neighboring  particles.  In  the 
earlier  stage,  on  the  contrary,  only  a  portion  of  the  heat  received 
by  a  particle  is  thus  disposed  of,  the  remainder  being  accumu- 
lated in  the  particle,  and  serving  to  raise  its  temperature. 

212.  Conducting  Power  of  Solids.  —  Different  solids  are 
found  to  vary  much  in  conductivity,  or  conducting  power. 

The  following  experiments  are  often  adduced  in  illustration 
of  the  different  conducting  powers  of  different  solids. 

Fig.  142. 


Two  bars  of  the  same  size,  but  of  different  materials  (Figure 
142),  are  placed  end  to  end,  and  small  wooden  balls  are  attached 


NATURAL    PHILOSOPHY.  141 

by  wax  to  the  under  surfaces  at  equal  distances.  The  bars  are 
then  hc.ited  at  their  contiguous  ends,  and,  as  the  heat  extends 
along  them,  the  wax  melts,  and  the  balls  successively  drop  off. 
If  the  heating  is  continued  till  the  permanent  state  arrives,  it 
may  generally  be  concluded  that  the  bar  which  has  lost  most 
balls  is  the  best  conductor. 

The  apparatus  shown  in  Figure  143  consists  of  a  copper  box 
having  on  one  side  a  row  of  holes  in  which  rods  of  different 
materials  can  be  fixed.  Fig  I43 

The  rods  having  been  pre- 
viously coated  with  wax, 
the  box  is  filled  with  boil- 
ing water,  which  comes 
into  contact  with  the  inner 
ends  of  the  rods.  The 
wax  gradually  melts  as  the  heat  travels  along  the  rods ;  and  if 
the  experiment  is  continued  till  the  melting  reaches  its  limit, 
those  rods  on  which  it  has  extended  furthest  are,  generally 
speaking,  the  best  conductors.  It  is  thus  found  that  different 
metals  are  not  equally  good  conductors  of  heat,  and  that  the 
more  familiar  ones  may  be  arranged  in  the  following  order, 
beginning  with  the  best  conductors  :  Silver,  copper,  gold,  brass, 
tin,  iron,  lead,  platinum  ^  bismuth. 

Metals,  though  differing  considerably  one  from  another,  are 
as  a  class  greatly  superior  in  conductivity  to  other  substances, 
such  as  wood,  marble,  brick,  etc.  This  explains  several  familiar 
phenomena.  If  the  hand  is  placed  upon  a  metal  plate  at  the 
temperature  of  50°,  or  plunged  into  mercury  at  this  temperature, 
a  very  marked  sensation  of  cold  is  experienced.  This  sensation 
is  less  intense  with  a  block  of  marble  at  the  same  temperature, 
and  still  less  with  a  piece  of  wood.  The  reason  is  that  the 
hand,  which  is  at  a  higher  temperature  than  the  substance  to 
which  it  is  applied,  gives  up  a  portion  of  its  heat,  which  is  con- 
ducted away  by  the  substance ;  consequently  a  larger  portion  of 
heat  is  parted  with  in  the  case  of  the  body  of  greater  conducting 
power. 

213.  Conducting  Power  of  Liquids.  —  With  the  exception 
of  mercury  and  other  melted  metals,  liquids  are  exceedingly 


142 


ELEMENTS    OF 


Fig.  144. 


bad  conductors  of  heat.  This  can  be  shown  by  heating  the 
upper  part  of  a  column  of  liquid,  and 
observing  the  variations  of  tempera- 
ture below.  These  will  be  found  to  be 
scarcely  perceptible,  and  to  be  very 
slowly  produced.  If  the  heat  were 
applied  below  (Figure  144),  we  should 
have  the  process  called  convection  of 
heat ;  the  lower  layers,  made  lighter 
by  expansion,  would  rise  to  the  sur- 
face, and  be  replaced  by  colder  ones 
from  above,  which  would  be  heated 
and  rise  in  their  turn,  the  circulation 
thus  producing  a  general  heating  of 

the  liquid.     When  heat  is  applied  above,  the  expanded 

layers  remain  in  their  place,  and  the  rest  of  the  liquid  can 

be  heated  only  by  conduction  and  radiation. 

The  following  experiment  is  an  illustration  of  the  very  feeble 
conducting  power  of  water.     A  piece  of  ice  is  placed  at  the 

bottom  of  a  glass  tube  (Figure 
145),  which  is  then  partly  filled 
with  water  ;  heat  is  applied  to 
the  middle  of  the  tube,  and  the 
upper  portion  of  the  water  may 
be  made  to  boil  without  melting 
the  ice  below. 

2 1 4.  Conducting  Power  of 
Gases.  —  Of  the  conducting 
power  of  gases  it  is  almost 
impossible  to  obtain  any 
direct  proofs,  since  it  is  ex- 
ceedingly difficult  to  prevent 
the  interference  of  convec- 
tion and  direct  radiation. 
We  know,  however,  that  they 


Fig.  145- 


NATURAL    PHILOSOPHY.  143 

are  exceedingly  bad  conductors.  In  fact,  in  all  cases  where 
^ases  are  enclosed  in  small  cavities  where  their  movement 

t5 

is  difficult,  the  system  thus  formed  is  a  very  bad  conductor 
of  heat.  This  is  the  cause  of  the  feeble  conducting  powers 
of  many  kinds  of  cloth,  of  fur,  eider-down,  felt,  straw,  saw- 
dust, etc.  Materials  of  this  kind,  when  used  as  articles  of 
clothing,  are  commonly  said  to  be  warm,  because  they 
hinder  the  heat  of  the  body  from  escaping.  If  a  garment  of 
eider-down  or  fur  were  compressed  so  as  to  expel  the 
greater  part  of  the  air,  and  to  reduce  the  substance  to  a 
thin  sheet,  it  would  be  found  to  be  a  much  less  warm  cov- 
ering than  before,  having  become  a  better  conductor.  We 
thus  see  that  //  is  the  presence  of  air  which  gives  these  sub- 
stances their  feeble  conducting  power,  and  we  are  accordingly 
justified  in  assuming  that  air  is  a  very  bad  conductor  of 
heat. 

B.  CONVECTION. 

215.  Convection  Currents. —  Although  liquids  and  gases 
are  very  poor  conductors  of  heat,  they  allow  heat  to  be 
distributed    through   them    readily   by   convection    currents. 
When  heat  is  applied  to  any  portion  of  a  fluid,  the  heated 
portion    expands,    becomes    lighter,    and    rises,   allowing 
colder  portions   to  take  its  place   and  become  heated  in 
turn  ;  that  is,  the  system  of  currents  shown  by  the  arrows 
in  Figure  144  is  formed.     There  will  be  an  upward  cur- 
rent at  the  centre  of  the  heated  region,  an  outflow  in  every 
direction  above,  downward  currents  on  every  side,  and  an 
inflow  from    every  direction  below.     It  is  chiefly  in   this 
manner  that  heat  is  distributed  through  liquids  and  gases. 

C.  RADIATION  AND  ABSORPTION. 

216.  Illustration  of  Radiation.  —  When  two   bodies  at 
different  temperatures  are  brought  opposite  to  each  other, 
an  unequal  exchange  of  heat  takes  place  through  the  inter- 


144 


ELEMENTS    OF 


vening  distance  ;  the  temperature  of  the  hotter  body  falls, 
while  that  of  the  colder  rises,  and  after  some  time  the  tem- 
perature of  both  becomes  the  same.  This  propagation  of 
heat  across  an  intervening  space  is  what  is  meant  by  radia- 
tion, and  the  heat  thus  transmitted  is  called  radiant  heat. 
Instances  of  heat  communicated  by  radiation  are  the  heat 
of  a  fire  received  by  a  person  sitting  in  front  of  it,  and 
the  heat  which  the  earth  receives  from  the  sun. 

217.  Radiations  will  traverse  a  Vacuum. — This  last  in- 
stance shows  us  that  radiation  as  a  means  of  propagating  heat 
is  independent  of  any  ponderable  medium.  But  since  the  solar 
heat  is  accompanied  by  light,  it  might  still  be  questioned  whether 
non-luminous  heat  could  in  the  same  way  be  propagated  through 
a  vacuum. 

This  was  tested  by  Rumford  in  the  following  way.  He  con- 
Fig.  146.  structed  a  barometer,  the  upper  part  of  which 
was  expanded  into  a  globe  (Figure  146).  A 
thermometer  was  hermetically  sealed  into  the 
top,  so  that  the  bulb  of  the  thermometer  was  at 
the  centre  of  the  globe.  The  globe  was  thus 
a  Torricellian  vacuum-chamber.  By  melting 
the  tube  with  a  blow-pipe,  the  globe  was  sep- 
arated, and  was  then  immersed  in  a  vessel 
containing  hot  water,  when  the  thermometer 
immediately  rose  to  a  temperature  higher  than 
could  be  clue  to  the  conduction  of  heat  through 
the  stem.  The  heat  had  therefore  been  com- 
municated by  direct  radiation  -through  the 
vacuum  between  the  sides  of  the  globe  and  the 
bulb  a  of  the  thermometer. 

218.  Radiant  Heat  travels  in  Straight 
Lines.  —  In  a  uniform  medium  the  radiation  of  heat  takes 
place  in  straight  lines.  If,  for  instance,  between  a  ther- 
mometer and  a  source  of  heat  there  are  placed  a  number 
of  screens,  each  pierced  with  a  hole,  and  if  the  screens  are 
so  arranged  that  a  straight  line  can  be  drawn  through  the 
holes  from  the  source  to  the  thermometer,  the  temperature 


NATURAL    PHILOSOPHY.  145 

of  the  latter  immediately  rises  ;  if  a  different  arrangement 
is  adopted,  the  heat  is  stopped  by  the  screens,  and  the 
thermometer  indicates  no  effect. 

The  heat  which  travels  along  any  one  straight  line  is 
called  a  ray  of  heat.  Thus,  we  say  that  rays  of  heat  issue 
from  all  points  of  the  surface  of  a  heated  body,  or  that 
Mich  a  body  emits  rays  of  heat. 

219.  Molecular    Theory  of  Radiation.  —  According  to    the 
molecular  theory,  radiations  originate  in  the  vibrations  of  the 
atoms  within  the   molecule.     Each   kind   of   atoms  seems    to 
have   certain   characteristic  rates  of  vibration,  and  when   the 
molecules  in  their  motions  come  into  collision,  their  atoms  are 
thrown   into  vibration  ;   these  vibrations  are   communicated  to 
the  surrounding  ether  (3),  and  are  propagated  through  the  ether 
in  minute  waves  and  with  enormous  velocity.     As  the  tempera- 
ture of  the  body  rises  the  agitation  of  its  molecules  becomes 
more  energetic,  and  the  more  violent  collisions  of  the  molecules 
produce   more   powerful   vibration   of   the   atoms.     Hence  the 
radiation  becomes  more  intense  as  the  temperature  rises. 

220.  Different  Kinds  of  Radiation. — At  low  tempera- 
tures bodies  emit  only  obscure  radiations.     When  the  tem- 
perature reaches  a  certain  point,  the  body  becomes  red-hot, 
and  begins  to  emit  luminous  radiations.     At  a  still  higher 
temperature  it  becomes  white-hot. 

221.  Diathermanous  Bodies. — A  body,  like  air,  which  will 
allow   thermal  rays  to  pass  readily  through  it  is   said  to  be 
diathermanous.     If  a  polished  plate  of  glass  is  held  in  front  of 
a  body  heated  to  dull  redness,  it  will  stop  nearly  all  the  heat 
emitted  by  it.     If  the  same  plate  of  glass  is  held  in  front  of  a 
body  at  bright  white  heat,  it  will  allow  considerable  heat  to  pass 
through  it.     Glass  is  diathermanous  to  luminous  radiations,  but 
only  slightly  so  to  obscure  thermal  radiations.     A  solution  of 
alum    is    still    less   diathermanous    to   obscure    thermal    rays, 
although  it  allows  the  luminous  rays  to  pass  readily  through  it. 
A  solution  of  iodine  in  bisulphide  of  carbon,  on  the  contrary,  is 
perfectly  diathermanous  to  the  obscure  thermal  rays  and  per- 


146  ELEMENTS   OF 

fectly  opaque  to  the  luminous  rays.     A  polished  plate  of  rock 
salt  is  diathermanous  to  both  the  obscure  and  luminous  rays. 

222.  The  Effect  of  Rise  of  Temperature  on  Radiation.  — 
If  the  temperature  of  a  body  is  gradually  raised  to  the  highest 
possible  point,  and  a  cell  of  the  iodine  solution  is  used  to  cut 
off  the  luminous  radiations,  the  obscure  thermal  radiations  will 
be  found  to  grow  more  and  more  intense,  both  before  and  after 
the  body  begins  to  emit  luminous  radiations.  A  rise  of  tempera- 
ture, then,  has  two  effects  upon  the  radiation  of  a  body  ;  it  causes 
its  obscure  radiations  to  become  more  intense,  and  gives  rise  to 
new  radiations.  The  latter  radiations  differ  from  the  former  in 
having  quicker  vibrations  and  shorter  waves.  The  radiations 
of  longest  and  shortest  wave-lengths  are  obscure,  while  those  of 
medium  wave-lengths  are  luminous.  The  radiations  of  all 
wave-lengths  are  thermal,  but  the  thermal  power  is  greatest  in 
radiations  of  long  wave-lengths,  and  least  in  those  of  short 
wave-lengths.  All  radiations  are  capable  of  producing  certain 
chemical  effects,  but  the  chemical  or  actinic  power  is  least  in 
radiations  of  long  waves  and  greatest  in  the  short  waves.  The 
radiations  of  bodies  have,  accordingly,  been  divided  into  three 
classes  ;  namely,  obsciire  thermal,  luminous,  and  obscure  actmic. 
At  low  temperatures  bodies  emit  only  the  first  class  of  radia- 
tions ;  at  higher  temperatures,  the  first  and  second  classes  ;  and 
at  still  higher  temperatures,  all  three  classes. 

223.  Absorption. — Absorption  is  the  reverse  of  radiation. 
When  the  minute  waves  of  the  ether  encounter  the  mole- 
cules of  gross  matter,  they  throw  the  atoms  into  vibration, 
provided  they  can  vibrate  at  the  same  rate  as  the  particles 
of  the  ether  in  the  waves.     In  this  way  the  rays  are  taken 
up  and  absorbed  by  bodies.     It  is  only  those  rays  which 
are  absorbed  by  a  body  that  heat  it.    Bodies  are  not  warmed 
at  all  by  the  rays  which  they  transmit. 

224.  Good   Radiators   are    Good  Absorbers.  —  Rough 
blackened  surfaces  are  better  radiators  than  smooth  pol- 
ished surfaces,  and  they  are  also  better  absorbers. 

This   may  be   shown  by  the   following  experiment.      Two 
metallic  plates  A  and  B  (Figure   147)  of  the  same   size   are 


NATURAL    PHILOSOPHY. 


mounted  on  standards  which  move  to  and  fro  on  a  sliding 
bar  at  the  bottom.  Between  these  plates  there  is  a  rod  for 
supporting  a  ball  at  the  height 
of  the  centre  of  the  plates.  A 
is  coated  with  polished  nickel 
on  both  sides,  and  B  with  nickel 
on  one  side  and  lampblack  on 
the  other.  B  is  made  to  turn 
on  its  standard  so  that  the  sur- 
face coated  with  lampblack  may 
be  turned  either  towards  the 
ball  or  from  it.  First,  turn  the 
nickel  faces  of  the  plate  towards  the  ball,  heat  the  ball  to  dull 
redness,  place  it  upon  its  rod,  and  move  both  plates  up  against 
it  so  that  they  may  be  heated  equally.  Place  a  differential  ther- 
mometer (179)  as  shown  in  the  figure,  so  that  its  bulbs  shall  be 
equally  distant  from  the  two  plates.  One  of  the  bulbs  will 
be  heated  by  radiation  from  the  nickel  surface,  and  the  other 
by  radiation  from  the  blackened  surface.  The  liquid  in  the 
stem  will  move  towards  the  former  bulb,  showing  that  the  latter 
bulb  is  hotter,  and  that  the  radiation  is  more  powerful  from  the 
blackened  surface.  Now  reverse  plate  B,  turning  its  blackened 
face  towards  the  ball,  remove  the  ball,  and  allow  both  plates  to 
cool.  Place  each  plate  against  one  of  the  bulbs  of  the  ther- 
mometer, and  arrange  them  so  that  they  shall  be  equally  distant 
from  the  ball.  Heat  the  ball  and  replace  it  on  the  rod.  The 
plates  will  now  become  heated  by  absorption  of  radiations  from 
the  ball.  They  will  receive  equal  radiations,  but  the  thermome- 
ter will  indicate  that  the  plate  with  the  lampblack  coating 
towards  the  ball  is  the  hotter.  Hence  the  blackened  surf  ace  is 
the  better  absorber. 

Different  gases,  as  well  as  different  solids  and  liquids,  differ 
in  their  absorptive  power  and  in  the  kind  of  rays  which  they 
absorb.  Watery  vapor  among  gases  corresponds  to  glass 
among  solids  and  a  solution  of  alum  among  liquids.  It  is  dia- 
thermanous  to  luminous  rays,  but  much  less  so  to  obscure 
rays. 

Stoves  .and  radiators,  which  are  designed  to  give  out  heat, 
should  have  rough  blackened  surfaces ;  while  a  teapot,  which 


148  ELEMENTS   OF 

is  designed  to  keep  the  liquid  in  it  hot,  should  have  a  bright 
polished  surface. 

225.  Hot-Houses.  —  A  hot-house  is  a  structure  covered  with 
glass.  On  a  sunny  day  the  temperature  will  be  several  degrees 
higher  within  such  a  structure  than  on  the  outside.  The  lumi- 
nous heat  which  comes  from  the  sun  passes  readily  through  the 
glass  and  falls  upon  the  objects  within.  These  absorb  the  heat 
and  in  turn  send  back  obscure  heat.  This  heat  is  stopped  by 
the  glass.  Hence  the  heat  accumulates  within  the  hot-house. 
A  hot-house  may  be  described  as  a  trap  to  catch  sunbeams. 
Even  at  night  and  on  a  cold  cloudy  day  it  will  be  warmer  within 
a  hot-house  than  on  the  outside,  the  glass  preventing  the  ob- 
scure radiations  from  passing  off  into  space.  The  watery  vapor 
in  the  atmosphere  acts  just  like  the  glass  of  the  hot-house- 


NATURAL   PHILOSOPHY.  149 


IV. 

LIGHT. 

A.  RADIATION. 

226.  Luminous  Bodies.  —  Bodies,  like  a  gas-jet  or   the 
sun,  which  emit  light  of  their  own,  are  said  to  be  luminous. 
Light  is  now  believed  to  originate  in  extremely  minute  and 
rapid  vibrations  of  the  atoms  of   matter.     These  vary  in 
rapidity  from  about  400  million  million  to  about  760  million 
million  a  second.     The  atoms  of  all  luminous  bodies  are 
supposed  to  be  vibrating  at  this  enormous  rate. 

When  a  body  is  heated  its  atoms  are  thrown  into  more  and 
more  rapid  vibration,  and  when  the  rate  of  vibration  reaches 
400  million  million  a  second  the  body  begins  to  become  lumi- 
nous. In  the  case  of  a  candle-flame  or  gas-jet,  these  rapid 
vibrations  are  produced  by  the  clashing  of  the  atoms  of  oxygen, 
hydrogen,  and  carbon  as  they  rush  into  combination.  A  black- 
smith may  heat  a  nail  red-hot  by  vigorously  hammering  it. 
Each  blow  of  the  hammer  throws  the  atoms  of  the  nail  into 
more  rapid  vibration,  till  they  finally  vibrate  fast  enough  to 
develop  light. 

227.  Propagation  of  Light  by  the  Ether.  —  As  the  atoms 
of  matter  vibrate  in  the  ether  (3)  in  which  they  are  im- 
mersed,   they    communicate    their   vibration    to    it.     The 
vibrations  thus  started  are  propagated  through  the  ether  in 
every  direction  in  minute  waves  and  with  an  inconceivable 
velocity.     These  ethereal  waves  vary  in  length  according  to 
the  rate  gf  the  atomic  vibrations.    It  takes  somewhat  more 
than  35,000  of  the  longest  of  these  waves,  and  somewhat 


150  ELEMENTS    OF 

less  than  70,000  of  the  shortest,  to  make  the  length  of  an 
inch.  The  vibrations  are  transverse,  so  that  each  luminous 
wave  is  made  up  of  crest  and  hollow,  like  a  water  wave. 
Light  and  luminous  radiations  are  the  same  thing. 

228.  Velocity  of  Light.  —  The  velocity  of  light  is  about 
186,000  miles  a  second.  It  was  first  determined  by  Roemer, 
a  Danish  astronomer,  by  a  study  of  the  eclipses  of  one  of 
Jupiter's  moons.  He  found,  by  examining  a  long  series  of 
observations,  that  the  mean  interval  between  two  successive 
eclipses  of  the  moon  was  about  42^  hours,  but  that  the 
interval  varied  according  to  the  motion  of  the  earth  with 
respect  to  Jupiter.  When  the  earth  was  moving  away 

Fig.  148. 


from  Jupiter  from  T  to  T'  (Figure  148),  the  intervals 
were  longer  than  the  mean,  till  at  T'  the  eclipse  occurred 
about  16^2  minutes  late;  when  the  earth  was  moving 
towards  Jupiter,  from  T1  to  2]  the  intervals  were  shorter 
than  the  mean.  Now  we  cannot  be  aware  of  the  eclipse 
till  the  light  which  left  the  moon  just  as.it  entered  Jupiter's 
shadow  has  reached  the  earth ;  and  the  distance  this  light 
has  to  travel  is  continually  increasing  as  the  earth  travels 
from  T  to  T',  and  decreasing  as  the  earth  travels  from  T1' 
to  T.  Roemer  concluded  that  this  must  be  the  reason 
why  the  intervals  between  the  eclipses  were  longer  than 
the  mean  in  the  one  case  and  shorter  in  the  other.  As  the 


NATURAL    PHILOSOPHY.  151 

eclipse  occurred  16^  minutes  late  at  J7',  he  concluded 
that  it  must  take  light  about  i6*4  minutes  to  cross  the 
earth's  orbit.  As  this  distance  is  about  184,000,000  miles, 
light  must  travel  at  the  rate  of  about  186,000  miles  a  sec- 
ond. This  velocity  would  carry  light  around  the  earth  in 
about  %  of  a  second. 

Great  as  is  this  velocity,  it  is  believed  that  the  nearest  fixed 
star  is  so  distant  that  it  would  take  light  over  three  years  to 
reach  us  from  it,  while  the  most  distant  stars  are,  at  least,  a 
thousand  times  more  remote.  Were  all  the  stars  in  the  heavens 
blotted  out  of  existence  to-night,  it  would  be  over  three  years 
before  we  should  miss  any  of  them,  a  quarter  of  a  century  before 
we  should  miss  many,  and  thousands  of  years  before  we  should 
lose  them  all.  The  light  which  will  enter  our  eyes  as  we  glance 
at  some  star  to-night  probably  started  on  its  journey  before  the 
building  of  the  great  pyramids,  and  has  been  travelling  eight 
times  the  distance  around  the  earth  every  second  since. 

Fig.  I49. 


229.  Rectilinear  Propagation  of  Light.  —  When  sunlight 
enters  through  an  opening  into  a  darkened  room,  it  illu- 
mines the  dust  in  the  atmosphere  in  its  path,  which  may 
then  be  easily  traced.  This  path  is  always  found  to  be 


ELEMENTS    OF 


straight.  Light  always  traverses  a  homogeneous  medium  in 
straight  lines.  A  single  line  of  light  is  called  a  ray,  and  a 
collection  of  rays  a  beam. 

230.  Images  produced  by  Small  Apertures.  —  If  a  white 
screen  is  placed  opposite  a  small  opening  in  a  shutter  of  a 
darkened  room,  an  inverted  picture  of  the  outside  landscape 
will  be  formed  on  the  screen  (Figure  149).  The  smaller 
the  opening,  the  sharper  the  image. 

The  formation  of  this  image  is  due  to  the  rectilinear  propaga- 
tion of  light.    The  point  A  (Figure  150)  is  sending  out  rays  in  all 
Fig  150.  directions  in  straight  lines.     The  rays  from 

this    point  which    pass   through    the    small 
opening  must  fall  upon  A1  of  the  screen.    In 
the  same  way    the    rays  from  B  must  fall 
^^\  A  uP°n  B'.   As  A  sends  light  to  no  part  of  the 
o'\.  screen  except  A',  and  as  A'  receives  light 

\J  B  from  no  part  of  the  object  but  At  the  color 
and  brightness  of  the  spot  A'  will  depend 
upon  the  color  and  brightness  of  A  ;  in  other 
words,  A'  will  be  the  image  of  A.  In  like  manner  B'  will  be 
the  image  of  B,  while  the  points  of  the  object  between  A  and  B 
will  have  their  images  at  corresponding  points  between  A'  and 

Fig.  151. 


NATURAL    PHILOSOPHY. 


'53 


B'.    An  inverted  image  of  AB  will  thus  be  formed  between  A' 
and  B'. 

Hold  a  card  with  a  large  pin-hole  in  it  between  a  candle  and  a 
screen  (Figure  151),  and  an  inverted  image  of  the  candle  will  be 
formed  on  the  screen. 

Fig.  .52- 


When  the  sun  shines  through  a  small  hole  into  a  room  with 
the  blinds  closed,  whatever  may  be  the  shape  of  the  opening, 
the  image  of  the  sun  formed  on  the  floor  or  wall  will  be  round  or 
oval,  according  as  it  falls  upon  a  surface  which  is  perpendicular 
or  oblique  to  the  rays  (Figure  152).  When  the  sun  shines 
through  the  foliage  of  trees,  the  spots  of  light  on  the  ground 
will  always  be  round  or  oval,  whatever  may  be  the  shape  of  the 
openings  through  which  the  light  comes,  provided  they  are  suf- 
ficiently small.  When  the  sun  is  undergoing  eclipse,  the  progress 
of  the  eclipse  may  be  watched  by  noticing  the  shape  of  these 
spots,  which  will  always  be  that  of  the  uneclipsed  portion  of  the 
sun's  disc. 

231.  Shadows.  —  Bodies  which,  like  glass,  allow  light  to 
pass  readily  through  them,  are  said  to  be  transparent. 
Bodies  which  do  not  allow  light  to  pass  through  them  are 
said  to  be  opaque. 

Owing  to  the  rectilinear  propagation  of  light,  opaque 
bodies  in  front  of  a  light  must  necessarily  cast  shadows, 
that  is,  shut  off  the  light  from  some  of  the  space  behind  them. 


154  ELEMENTS    OF 

If  the  luminous  body  6"  (Figure  153)  is  a  mere  point,  the 
body  /I/will  cast  a  well-defined  shadow  GH  upon  the  screen 
PQ.  If  the  straight  line  SG  is  kept  fast  at  S,  and  carried  round 
the  sphere  J/,  touching  it  all  the  time,  it  will  describe  a  cone. 

Fig.  153- 


The  part  M  G,  as  it  passes  round,  will  exactly  mark  the  limits 
of  the  shadow  cast  by  M. 

If  the  luminous  body  is  not  a  mere  point,  the  shadow  of  M 
(Figure  154)  upon  the  screen  will  be  indistinct  in  outline. 

Prolong  the  line  GS  to  A.  Keep  the  point  A  fixed  and 
carry  the  line  A  G  around  the  spheres  S  and  M,  keeping  it  in 
contact  with  both.  The  line  will  describe  a  cone,  and  the  part 


Fig.  154- 


M  G  will  mark  out  the  space  from  which  the  light  is  entirely  ex- 
cluded. This  is  called  the  iimbra  of  the  shadow.  If  the  line 
S C  is  kept  fixed  at  B,  and  then  carried  round  the  two  spheres, 
it  will  describe  a  double  cone,  whose  apex  will  be  at  B.  The 
partvVCof  this  line  will  mark  the  extreme  limits  of  the  shadow. 
From  the  part  outside  of  the  umbra  only  a  portion  of  the  light  is 
excluded^  and  the  farther  we  pass  from  the  umbra  the  less  the 
light  excluded.  This  part  of  the  shadow  is  called  the  penumbra. 
It  will  be  seen  at  once  from  the  figure,  that  the  light  from  S 
will  reach  all  the  space  between  D  and  G,  and  the  light  from  L 
all  the  space  between  Cand  //. 


NATURAL    PHILOSOPHY. 


232.  Illumination.  —  The  illuminating  power  of  a  source 
of  light  diminishes  as  the  square  of  the  distance  from  the  illu- 
minating body  increases. 

In  Figure  155  the  disc  CD  is  held  parallel  with  the  screen 
A  B<  and  half-way  between  the  screen  and  the  source  of  light 


L.  The  diameter  of  the  shadow  on  the  screen  will  be  twice  that 
of  the  disc,  and  the  area  of  the  shadow  four  times  that  of  the 
disc.  The  disc  receives  all  the  light  that  would  fall  upon  the 
space  covered  by  the  shadow,  were  the  disc  removed.  Hence 
the  illumination  of  the  disc  is  four  times  as  intense  as  that  of 
the  screen.  If  the  disc  were  held  one  third  of  the  way  from  L 
to  the  screen,  the  area  of  the  disc  would  be  one  ninth  that  of  its 
shadow,  and  the  illumination  of  the  disc  would  be  nine  times  as 
intense  as  that  of  the  screen. 

Fig.  156. 


233.  Photometry.  —  Photometry  is  the  measurement  of  the 
relative  illuminating  power  of  different  sources  of  light ;  and 
the  instrument  used  is  called  a  photometer. 


156  ELEMENTS    OF 

Riimf or ds  photometer,  based  upon  the  comparison  of  shadows, 
is  one  of  the  simplest  of  these  instruments.  An  opaque  rod  M 
(Figure  156)  is  placed  in  front  of  a  ground-glass  screen.  The 
lights  L  and  B  to  be  compared  are  placed  so  that  each  casts  a 
separate  shadow  of  the  rod  upon  the  screen.  These  distances 
are  then  made  such  that  the  two  shadows  a  and  b  are  of  exactly 
the  same  intensity.  The  screen  must  then  be  receiving  the 
same  illumination  from  each  light ;  for  the  shadow  cast  by  B  is 
illumined  by  L,  and  that  cast  by  L  is  illumined  by  B.  Hence 
the  illuminating  power  of  the  two  lights  will  be  to  each  other  as 
the  squares  of  the  distances  of  the  lights  from  the  screen. 

B.   REFLECTION. 

234.  Diffusion.  —  When  light  meets  the  surface  of  a  new 
medium,  a  portion  of  it  is  diffused,  that  is,  thrown  back  and 
scattered  irregularly  in  every  direction.     It   is   by  means  of 
the  light  thus  diffused  that  we  are  enabled  to  see  the  sur- 
faces of  non-luminous  bodies.     Smooth  polished  surfaces 
diffuse  less  light  than  rough   irregular  ones,  but   the  most 
highly  polished  mirror  diffuses  enough  light  to  enable  us  to 
see  its  surface,  though  sometimes  with  difficulty. 

235.  Reflection.  —  On  meeting  the  surface  of  a  new  me- 
dium, a  portion  of  the  light  is  reflected,  that  is,  thrown  back 

Fig  I57  in  a  definite  direction.      In  Figure  157 

IP  R  AB  represents  the  surface  of  the  new 
medium,  1C  the  ray  coming  to  it,  or 
the  incident  ray,  and  CR  the  reflected 
ray.  PC  is  a  perpendicular  to  the 

surface  of  the  medium  at  the  point  C.  The  angle  TCP  is 
called  the  angle  of  incidence,  and  the  angle  HCP'is  called 
the  angle  of  reflection. 

In  reflection,  the  angles  of  incidence  and  reflection  are 
always  equal.  The  smoother  the  surface  of  a  medium,  the 
greater  the  proportion  of  the  light  reflected  from  it.  Good 
reflecting  surfaces  are  called  mirrors. 


NATURAL    PHILOSOPHY.  157 

236.  Images  formed  by  Plane  Mirrors.  —  It  is  by  reflected 
light  that  we  see  images  of  objects  in  reflecting  surfaces. 
These  visible  images  formed  by  reflection  correspond  to  the 
echoes  formed  by  reflection  in  the  case  of  sound. 

Figure  158  represents  a  pencil  of  rays  emitted  from  the  highest 
point  of  a  candle-flame  to  the  Fig  i  g 

eye  of  an  observer.  The  rays 
have  exactly  the  same  degree 
of  divergence  after  reflection  as 
before,  and  if  prolonged  back- 
ward would  meet  just  as  far 
behind  the  mirror  as  the  point 
from  which  they  come  is  in  front 
of  it.  The  same  would  be  true 
of  the  rays  coming  from  every 
point  of  the  object.  Hence  an  image  seen  in  a  plane  mirror  will 
seem  just  as  far  behind  the  mirror  as  the  object  is  in  front  of  it. 
This  is  not  only  true  of  the  image  as  a  whole,  but  also  of  each 
part  of  it. 

Fig-  159- 


237.  Images  formed  by  two  Mirrors  at  an  Angle  to  each 
other.  —  Figure  159  shows  the  images  that  would  be  formed  by 
two  mirrors  at  right  angles  to  each  other,  one  being  horizontal 
and  the  other  vertical. 

Figure  160  shows  the  images  that  would  be  formed  if  an  ob- 


'58 


ELEMENTS    OF 


ject  were  placed  between  two  mirrors  facing  each  other  at  an 
Fig.  j6o-  angle   of   60°.      When  the  mirrors 

are  inclined  to  each  other,  the  im- 
ages formed  are  always  arranged 
in  the  circumference  of  a  circle, 
whose  centre  is  at  the  intersection 
of  the  mirrors,  while  its  circum- 
ference passes  through  the  object. 

238.  The  Kaleidoscope.  —  The 
kaleidoscope  is  an  optical  toy,  in- 
vented by  Sir  David  Brewster.  It 
consists  of  a  tube  containing  two 
glass  plates,  extending  along  its  whole  length,  and  inclined  at 
an  angle  of  60°.  One  end  of  the  tube  is  closed  by  a  metal 
plate,  with  a  hole  in  the  centre,  through  which  the  observer 

looks  in;  at  the  other  end 
there  are  two  plates,  one  of 
ground  and  the  other  of 
clear  glass  (the  latter  being 
next  the  eye),  with  a  num- 
ber of  little  pieces  of  colored 
glass  lying  loosely  between 
them.  These  colored  ob- 
jects, together  with  their 
images  in  the  mirrors,  form 
symmetrical  patterns  of 
great  beauty,  which  can  be 
varied  by  turning  or  shak- 
ing the  tube,  so  as  to  cause 
the  pieces  of  glass  to  change  their  positions  (Figure  161). 

C.   REFRACTION. 

239.  Refraction.  —  If  a  beam  of  light  is  allowed  to  fall 
obliquely  upon  water,  it  will  be  seen  to  be  bent  on  enter- 
ing the  water,  though  it  will  continue  to  move  on  in  a 
straight  line  after  it  has  passed  into  the  water.  This 
bending  of  a  ray  of  light,  in  passing  obliquely  from  one  me- 
dium to  another,  is  called  refraction. 


NATURAL    PHILOSOPHY. 


'59 


Fig.  163. 


If  a  coin  or  other  object  m  n  (Figure  162)  is  placed  on  the 
bottom  of  a  vessel  with  Fig.  ,62- 

opaque  sides,  so  as  just  to  be 
concealed  from  an  eye  at  O, 
and  the  vessel  is  then  filled 
with  water,  the  bottom  of 
the  vessel  will  seem  to  rise 
and  the  object  will  come 
into  view.  This  is  because 
the  pencils  of  rays  coming  from  the  object  at  m  will  be  suddenly 
bent  on  entering  the  air  and  will  reach  the  eye  as  if  they  came 
from  /«',  where  the  object  will  ap- 
pear to  be. 

For  a  similar  reason,  a  stick 
partly  immersed  in  water,  in  an 
oblique  position,  will  appear  bent, 
as  shown  in  Figure  163. 

When  a  ray  of  light  passes 
obliquely  from  a  rarer  into  a 
denser  medium,  it  is  bent  towards 
a  perpejidicular  drawn  to  the  sur- 
face of  the  medium  at  the  point  of  contact  of  the  ray. 

In  Figure  164  A  B  represents  the  surface  of  a  denser  me- 
dium, 1C  the  incident  ray,  C  R  the  refracted  ray,  and  P  C  H  a 
perpendicular  to  the  surface  of  the  medium  at  the  point  C.  The 

Fig-  '64-  Fig.  165. 

,p  U  IP 


angle  R  CH  is  the  angle  of  refraction.     In  this  case  the  angle  of 
refraction  is  less  than  the  angle  of  incidence. 

When  a  ray  of  light  enters  a  rarer  medium  obliquely,  it 
is  bent/ram  a  perpendicular  to  the  surface  of  the  medium  at 
the  point  of  contact. 


i6o 


ELEMENTS    OF 


In  Figure  165  A  B  represents  the  surface  of  a  rarer  medium, 
/Cthe  incident  ray,  C R  the  refracted  ray,  and  P  C H  the  per- 
pendicular. In  this  case  the  angle  of  refraction  is  greater  than 
the  angle  of  incidence. 

When  a  ray  of  light  enters  any  medium  perpendicularly, 
there  is  no  refraction. 

240.  Total  Reflection.  —  The  angle  of  incidence  may 
have  any  value  from  o°  up  to  90°. 
When  light  enters  a  denser  medium, 
the  angle  of  refraction  is  less  than 
the  angle  of  incidence,  and  hence 
always  less  than  90°.  But  when 
!H  light  enters  a  rarer  medium,  there 

is  always  a  certain  angle  of  incidence  I C  P  (Figure  166) 
at  which  the  angle  of  refraction  H  C  R  is  equal  to  90°. 
F'g-  i67.  This  angle  is  called  the 

limiting  angle,  or  the 
critical  angle.  When 
the  media  are  air  and 
water,  this  angle  is 
about  48^  degrees. 
For  air  and  the  differ- 
ent kinds  of  glass  it 
ranges  from  38°  to  41°. 
When  the  angle  of 
incidence  exceeds  the 
limiting  angle,  none  of 
the  light  will  enter 
the  medium,  however 
transparent  it  may  be. 
'In  this  case  the  light 
will  be  totally  reflected, 
the  angle  of  reflection 
being  equal  to  that  of 
incidence. 


NATURAL    PHILOSOPHY.  l6l 

If  a  glass  of  water,  with  a  spoon  in  it,  is  held  above  the 
level  of  the  eye  (Figure  167),  the  under  side  of  the  surface  of 
the  water  is  seen  to  shine  like  polished  silver,  and  the  lower  part 
of  the  spoon  is  seen  reflected  in  it.  The  rays  of  light  which 
pass  upward  through  the  water  at  a  certain  angle  are  totally  re- 
flectedon  meeting  the  air. 

D.    DISPERSION. 

241.  The  Dispersion  Spectrum.  —  If  a  glass  prism  (Fig- 
ure 1 68)  is  held  with  its  edge  down  to  the  path  of  a  thin 
beam  of  light,  the  spot  of  light  on  the  screen  will  be  raised 

kFig.  168. 


and  be  changed  into  a  beautifully  colored  band,  in  which 
the  colors  are  arranged  in  the  order  of  red,  orange,  yellow, 
green,  blue,  indigo,  and  violet.  The  colored  band  produced 
by  the  passage  of  a  beam  of  light  through  a  prism  is  called 
the  dispersion  spectrum.  The  raising  of  the  spot  of  light  on 
the  screen  is  due  to  the  bending  of  the  beam  as  a  whole 
by  the  prism  ;  and  the  formation  of  the  colored  band,  to 
the  unequal  bending  of  the  different  colored  rays  of  which 
white  light  is  composed,  red  being  bent  the  least  and  violet 
the  most  of  all  the  rays.  The  separation  of  the  colored  rays 
by  refraction  is  called  dispersion. 

The  refrangibility  of  light  is  found  to  depend  upon  the  length 
of  its  waves ;  the  shorter  the  waves,  the  more  refrangible  the 
ray.  The  violet  rays  are  more  refrangible  than  the  red  because 
they  have  shorter  waves. 

II 


1 62  ELEMENTS    OF 

In  the  case  of  sunlight  and  of  light  from  any  intense  source 
of  heat,  it  is  found  that  the  thermal  or  heating  powe'r  of  the 
spectrum  extends  considerably  beyond  the  red,  and  the  actinic 
or  chemical  power  considerably  beyond  the  violet.  The  com- 
plete spectrum  is  composed  of  three  parts,  a  luminous  portion 
at  the  centre,  an  obscure  thermal  portion  beyond  the  red,  and  an 
obscure  actinic  portion  beyond  the  violet.  Every  portion  of  the 
spectrum  is  thermal,  but  the  thermal  power  increases  rapidly  as 
we  approach  the  red  end,  and  is  greatest  just  beyond  the  red. 
Every  part  of  the  spectrum  is  also  actinic,  but  the  greatest 
actinic  power  is  in  the  region  of  the  blue.  Only  the  central  part 
of  the  spectrum  is  luminous,  and  the  greatest  luminosity  is  in 
the  region  of  the  yellow  and  green. 

242.  Achromatic  and  Direct-  Vision  Prisms.  —  The  refractive 
power  of  a  substance  is  independent  of  its  dispersive  power. 
Hence,  by  using  different  kinds  of  glass,  it  has  been  found  pos- 
sible to  construct  prisms  which  shall  have  equal  refractive  powers 
and  unequal  dispersive  powers,  or  equal  dispersive  and  unequal 
refractive  powers.  If  two  prisms  of  crown  and  flint  glass  are 
constructed  so  as  to  have  equal  powers  of  bending  a  beam  of 
light  as  a  whole,  the  flint-glass  prism  will  produce  greater  dis- 
persion than  the  crown-glass.  If,  on  the  other  hand,  the  two 
prisms  are  constructed  so  as  to  produce  equal  dispersion,  the 
crown-glass  prism  will  bend  the  ray  as  a  whole  more  than  the 
flint-glass. 

When  two  prisms  of  equal  dispersive  and  unequal  refractive 
powers  are  combined,  with  the  thicker  part  of  one  beside  the 
thinner  part  of  the  other  (Figure  169),  they  form  what  is  called 
Fig.  169.  an  achromatic  prism.     Such  a  prism 

produces  refraction  without  disper- 
sion. Achromatic  means  'without 
color. 

When  two  prisms  of  equal  re- 
fractive and  unequal  dispersive 
powers  are  combined  as  above, 
they  form  what  is  known  as  a 
direct-vision  prism.  Such  a  prism 

produces    dispersion    without    refraction.      In     using    it    we 
look    directly   at  the   object,  while   with    any  other  prism  we 


NATURAL    PHILOSOPHY.  163 

are    obliged  to  look   somewhat  away   from   the  object    (Fig- 
ure 170). 

Fig.  170. 


243.  The  Spectroscope.  —  The  spectroscope  is  an  instrument 
for  examining  spectra.     A   simple  spectroscope  is  shown   in 
Fig.  171. 


Figure  171.     The  tube  at  the  right  is  called  the  collimator  tube. 


164  ELEMENTS    OF 

The  light  to  be  examined  is  admitted  through  a  narrow  opening 
at  the  end  of  the  tube,  and  the  rays  are  rendered  parallel  by 
means  of  a  lens  within  it.  The  light  is  then  dispersed  by  the 
prism,  and  the  spectrum  examined  by  means  of  the  telescope  at 
the  left  of  the  prism.  The  tube  in  front  of  the  prism  has  a  scale 
engraved  on  glass  in  the  opening  at  the  end  next  to  the  candle. 
The  light  from  the  candle  which  shines  through  this  scale  is 
reflected  from  the  side  of  the  prism  into  the  telescope,  so  as  to 
form  an  image  of  the  scale  alongside  that  of  the  spectrum. 

244.  Three  Kinds  of  Spectra.  —  On  examining  with  the 
spectroscope  the  light  from  an  incandescent  solid,  its  spectrum 
will  be  found  to  be  a  continuous  band  of  colors,  changing  by  in- 
sensible gradations  from  red  at  one  end  to  violet  at  the  other. 
Such  a  spectrum  is  called  a  continuous  spectrum.  Incandescent 
solids  and  liquids  give  continuous  spectra. 

If  we  examine  with  the  spectroscope  the  light  from  lumi- 
nous strontium  vapor,  its  spectrum  (see  frontispiece)  will  be 
seen  to  be  made  up  of  bright  lines  and  dark  spaces.  Such  a 
spectrum  is  called  a  bright-lined  or  broken  spectrum.  Vapors 
and  gases,  when  luminous,  give  bright-lined  spectra.  The 
spectra  of  different  gases  and  vapors  differ  in  the  number  and 
position  of  these  lines.  Hence  a  vapor  may  be  recognized  by 
its  spectrum. 

The  dark  spaces  of  these  spectra  are  due  to  the  absence  of 
certain  rays.  While  incandescent  solids  and  liquids  emit  rays 
of  all  degrees  of  refrangibility,  luminous  vapors  and  gases  emit 
those  only  of  particular  degrees  of  refrangibility.  Each  vapor 
or  gas  emits  just  as  many  sets  of  rays  as  there  are  bright  lines 
in  its  spectrum.  The  number  of  these  lines  ranges  from  one  up 
to  several  hundred. 

The  analysis  of  light  by  means  of  the  spectroscope  is  called 
spectrum  analysis.  The  spectrum  of  an  incandescent  solid  or 
liquid,  when  shining  through  a  luminous  vapor  or  gas,  is  made 
up  of  dark  lines  separated  by  bright  spaces,  there  being  a  dark 
line  for  every  bright  line  which  the  gas  alone  would  give.  Such 
spectra  are  called  reversed  spectra,  the  spectrum  of  the  gas  being 
reversed  by  the  light  of  the  solid  which  passes  through  it. 


NATURAL   PHILOSOPHY. 


E.   LENSES. 

245.  Forms  of  Lenses.  —  A  lens  is  a  transparent  medium 
having  at  least  one  curved  side.  Lenses  are  usually  made 
of  glass,  and  are  circular  in  outline.  Their  curved  sur- 
faces are  usually  spherical.  They  are  divided  into  two 
classes,  according  to  their  shape,  namely,  convex  lenses  and 
concave  lenses.  Every  convex  lens  has  at  least  one  convex 
surface,  and  is  thickest  at  the  centre;  and  every  concave 
lens  has  at  least  one  concave  surface,  and  is  thickest  at  the 
margin.  There  are  three  forms  of  each  class  of  lenses. 
These  six  forms  of  lenses  are  shown  in  section  in  Figure 

Fig.  172. 

C  D 


172.  The  first  three  are  convex  and  the  last  three  con- 
cave lenses.  A  is  a  double-convex  lens,  having  two  convex 
surfaces.  B  is  a  plano-convex  lens,  having  one  plane  and 
one  convex  surface.  C  is  a  concavo-convex  lens,  having  a 
concave  and  a  convex  surface,  the  convex  surface  having 
the  greater  curvature.  This  lens  is  often  called  a  meniscus^ 
D  is  a  double-concave  lens,  having  two  concave  surfaces. 
E  is  a  plano-concave  lens,  having  a  plane  and  a  concave 
surface.  F  is  a  convexo-concave  lens,  having  a  convex  and 
a  concave  surface,  the  concave  surface  having  the  greater 
curvature. 

246.  The  Optical  Centre  of  a  Lens.  —  There  is  for  every 
lens  a  point,  any  straight  line  drawn  through  which  will  meet 
on  opposite  sides  of  the  lens  portions  of  surface  which  are  par- 
allel. This  point  is  called  the  optical  centre  of  the  lens. 


1 66  ELEMENTS   OF 

247.  Axes  and  Foci  of  Lenses,  —  Any  straight  line  drawn 
through  the  optical  centre  of  a  lens  is  called  an  axis.     An 
axis  which  passes  through  the  centre  of  curvature  of  a  lens 
is  called  the  principal  axis,  and  every  other  axis  a  second- 
ary axis. 

Every  ray  of  light  which  coincides  with  an  axis  will  emerge 
from  a  lens  with  the  same  direction  it  had  before  entering,  since 
it  will  pass  through  a  portion  of  a  medium  having  parallel  sides. 
Every  other  ray  which  passes  through  a  lens  will  be  deflected 
towards  the  thicker  part  of  the  lens.  In  the  case  of  a  convex 
lens  the  deflection  will  be  towards  the  centre  of  the  lens,  and  of 
a  concave  lens  towards  the  margin. 

When  the  rays,  on  emerging  from  a  lens,  are  either 
convergent  or  divergent,  the  points  towards  which  they  con- 
verge or  from  which  they  diverge  are  called  foci.  When  the 
rays  are  convergent  on  emerging  from  the  lens,  the  focus  is 
real ;  and  when  they  are  divergent,  it  is  virtual. 

248.  Parallel  Rays   with   Lenses.  —  Parallel  rays   with    a 

convex  lens  (Figure  173)  become 
convergent  on  emerging  from  the 
lens,  and  have  a  real  focus  on 
the  opposite  side  of  the  lens  to 
that  on  which  they  enter  and  on 
the  axis  to  which  the  rays  are 
parallel. 
Parallel  rays  with  a  concave  lens  (Figure  174)  become  di- 

Fig.  I74. 


vergent,  and  have  a  virtual  focus  on  the  same  side  of  the  lens 
as  that  on  which  the  rays  enter  and  on  the  axis  to  which  the 


rays  are  parallel. 


NATURAL   PHILOSOPHY. 


i67 


249.  Principal  Foci  and  Focal  Length.  —  The  focus  for 
parallel  rays  is  called  the  principal  focus  of  the  lens.  It 
may  be  real  or  virtual,  and  on  the  principal  axis  or  on  a 
secondary  axis.  The  distance  from  the  optical  centre  of  a 
lens  to  the  principal  focus  is  called  the  focal  length  of  the 
lens.  The  greater  the  curvature  of  a  lens,  and  the  greater 
the  refractive  power  of  the  material  of  which  it  is  com- 
posed, the  shorter  the  focal  length  of  the  lens. 

Fig.  175. 

A 


250.  Divergent  Rays  -with  Lenses.  —  Divergent  rays  with  a 
convex lens  (Figure  175),  the  point  of  divergence  being  beyond 
the  focal  length  of  the  lens,  become  convergent  on  emerging  from 
the  lens,  and  have  a  real  focus  on  the  opposite  side  of  the  lens 
to  that  on  which  the  rays  enter,  on  the  same  axis  as  the  point 
of  divergence,  and  at  a  distance  greater  than  the  focal  length. 

Divergent  rays  with  a  convex  lens  (Figure  176),  when  the 


Fig.  176. 


point  of  divergence  is  within 
the  focal  length  of  the  lens, 
become  less  divergent  on 
emerging  from  the  lens,  and 
have  a  virtual  focus  on  the 
same  side  of  the  lens  as  that 
on  which  the  rays  enter,  on  the  same  axis  as  the  point  of  di- 
vergence, and  at  a  distance  from  the  lens  greater  than  that  of 
the  point  of  divergence. 

Fig.  177.  Fig.  178. 


Divergent  rays  with  a  concave  lens  (Figure  ^7)  become  more 
divergent,  and  have  a  virtual  focus  on  the  same  side  of  the  lens 


1 68  ELEMENTS   OF 

as  that  on  which  the  rays  enter,  on  the  same  axis  as  the  point  of 
divergence,  and  nearer  the  lens. 

251.  Convergent  Rays  with  Lenses.  —  Convergent  rays  with 
a  concave  lens,  the  point  of  convergence  C  (Figure  178)  being 
at  the  focal  length,  on  emerging  from  the  lens,  become  parallel 
with  the  axis  on  which  the  point  of  convergence  lies. 

When  the  point  of  convergence  is  beyond  the  focal  length  of 

Fig.  179. 


the  lens  (Figure  179),  the  rays,  being  less  convergent  on  meet- 
ing the  lens  than  in  the  previous  case,  become  divergent  on 
emerging  from  the  lens,  have  a  virtual  focus  on  the  same  side  of 
the  lens  as  that  on  which  the  rays  enter,  on  the  same  axis  as 
the  point  of  convergence,  and  farther  from  the  lens  than  the 
focal  length  of  the  lens. 

Fig.  180.  Convergent  rays  with  a  convex 

lens  (Figure  180)  become  more 
convergent  on  emerging  from  the 
lens,  and  have  a  real  focus  on  the 
opposite  side  of  the  lens  to  that  on 

3J—-"""'""  which  the  rays  enter,  on  the  same 

axis  as  the  point  of  convergence,  and  nearer  the  lens. 

252.  Images  formed  by  Lenses.  —  Rays  are  diverging 
from  every  point  on  the  surface  of  an  object ;  that  is  to 
say,  every  such  point  is  a  point  of  divergence.  The  focus  of 
a  point  is  a  copy  or  image  of  that  point,  and  the  foci  of  all 
the  points  on  the  surface  of  an  object  form  an  image  of  the 
object. 

To  find  the  image  of  an  object  it  is  necessary  to  find  only  the 
foci  of  its  extremities.  To  find  these  foci,  we  have  only  to  draw 
axes  through  the  extremities  of  the  object,  and  locate  the  foci 
on  these  axes,  according  to  the  case  of  divergent  rays  under 
which  they  come. 


NATURAL    PHILOSOPHY. 


i69 


(i.)  Figure  181  represents  the  case  of  an  object  AB 
beyond  the  focal  length  of  a  convex  lens.  The  image  a  b  is 
real,  because  made  up  of  real  Fig.  l8l. 

foci ;  inverted,  because  the  axes 
cross  between  the  image  and  the 
object ;  and  in  this  case  larger 
than  the  object,  because  farther 
from  the  lens.  Were  the  object  distant,  the  image  would  be 
nearer  than  the  object  to  the  lens,  and  consequently  smaller 
than  the  object.  The  nearer  the  object  to  the  principal  focus 
of  the  lens,  the  more  distant  and  tne  larger  the  image. 

(2.)  Figure  182  represents  the  case  of  an  object  A  B 
within  the  focal  length  of  a  convex  lens.  The  image  a  b  is 
virtual,  because  made  up  of  virtual  foci ;  erect,  because  the 
axes  do  not  cross  between  the  image  and  the  object ;  and 
larger  than  the  object,  because  farther  from  the  lens.  The 
nearer  the  object  to  the  principal  focus  of  the  lens,  the 
more  distant  and  the  larger  the  image. 


Fig.  182. 


Fig.  183. 


(3.)  Figure  183  represents  the  case  of  an  object  AB 
with  a  concave  lens.  The  image  ab  is  virtual,  because 
made  up  of  virtual  foci ;  erect,  because  the  axes  do  not 
cross  between  the  image  and  the  object ;  and  smaller  than 
the  object,  because  nearer  the  lens.  ' 

Virtual  images  can  be  seen  only  by  looking  through  the 
lens  at  the  object. 

253.  Magnifying  Power  of  Lenses.  —  (i.)  When  an  object 
is  40  or  50  feet  distant,  the  rays  from  it  which  fall  upon  a 
small  lens*are  sensibly  parallel,  and  are  brought  to  a  focus 


170 


ELEMENTS   OF 


nearly  at  its  focal  length.  The  image  of  a  distant  object 
is,  therefore,  formed  nearly  at  the  focal  length  of  a  lens ; 
hence  the  longer  the  focal  length  the  larger  the  image  of  such 
an  object. 

(2.)  When  we  can  place  the  object  very  near  the  princi- 
pal focus  of  the  lens,  the  shorter  the  focal  length  the  larger 
the  image  it  will  form. 

Fig.  184. 


This  is  readily  seen  from  Figure  184.  The  two  lenses  I  and 
2  are  represented  as  in  the  same  position.  F'  is  the  principal 
focus  of  the  first  lens,  and  F"  that  of  the  second  lens.  A  B 
represents  the  same  object  placed  near  the  principal  focus  of 
each  lens,  so  that  each  will  form  an  image  of  it  at  the  same  dis- 
tance on  the  other  side  of  the  lenses.  The  image  a'  £>',  formed 
by  the  first  lens,  is  seen  to  be  smaller  than  the  image  a" b", 
formed  by  the  second  lens. 

254.  Spherical  Aberration.  —  The  rays  which  pass  through 
an  ordinary  lens  near  the  margin  are  brought  to  a  focus  a 
little  nearer  the  lens  than  those  which  pass  through  near  the 
centre  (Figure  185).  This  action  of  the  lens  is  called 

Fig.  185.  Fig.  186. 


spherical  aberration.  It  causes  the  image  to  appear 
blurred.  It  is  obviated  by  grinding  the  lens  to  a  special 
form,  which  can  be  exactly  ascertained  only  by  trial. 

255.    Chromatic  Aberration.  —  An  ordinary  lens  not  only 


NATURAL    PHILOSOPHY. 


171 


refracts,  but  also  disperses  the  rays  of  light,  so  that  the 
violet  rays,  which  are  most  refrangible,  are  brought  to  a 
focus  at  i  (Figure  186),  while  the  red  rays,  which  are 
least  refrangible,  are  brought  to  a  focus  at  2.  pig.  is7. 
The  other  rays  are  brought  to  a  focus  between 
these  points.  This  action  of  the  lens  is  called 
chromatic  aberration.  It  causes  the  image  to 
be  fringed  with  colors.  It  can  be  overcome 
by  combining  a  convex  lens  of  crown  glass  with 
a  concave  lens  of  flint  glass,  which  has  an 
equal  dispersive  power,  but  a  smaller  refractive  power. 
Such  a  combination  of  lenses  (Figure  187)  is  called  an 
achromatic  lens. 

Fig.  188. 


256.    Concave  Mirrors   correspond  to    Convex   Lenses. — 
Lenses  act  by  refraction,  and  mirrors  by  reflection.     The 

Fig.  189. 


result  of  the  action  of  a  concave  mirror  on  rays  of  light 
is   the  same  as  that  of  a  convex  lens.     A  concave   mirror 


172  ELEMENTS    OF 

causes  parallel  rays  atter  reflection  to  converge  to  a  principal 
focus  (Figure  188);  rays  diverging  from  a  point  beyond  the 


principal  focus  to  become  convergent  (Figure  189)  ;  and  rays 
diverging  from  a  point  within  the  principal  focus  to  become 
less  divergent  (Figure  190). 

Fig.  191. 


It  follows  that  a  concave  mirror  will  form  the  same  im- 
ages as  a  convex  lens.  The  image  formed  by  such  a  mir- 
ror of  an  object  beyond  its  focal  length  (Figure  191)  is 
real  and  inverted;  while  the  image  of  an  object  placed 
within  its  focal  length  (Figure  192)  is  virtual,  erect,  and 
larger  than  the  object. 


NATURAL    PHILOSOPHY. 


To  avoid  spherical  aberration,  the  reflecting  surface  of 
a  concave  mirror  should  have  a  curvature  as  nearly  that  of 
the  parabola  as  possible.  Fig>  J<?2 

The  image  formed  by  a 
convex  mirror  is  virtual,  erect, 
and  smaller  than  the  object, 
as  in  the  case  of  a  concave 
lens. 

F.    OPTICAL  INSTRUMENTS. 

257.  The  Simple  Microscope. 
—  A  simple  microscope  consists 
of  a  convex  lens  mounted  in 
any  convenient  way.  The  ob- 
ject is  placed  a  little  within  its 
focal  length,  and  the  image 
seen  on  looking  through  the 
lens  is  virtual,  erect,  and 
larger  than  the  object.  The  shorter  the  focal  length  of  the 
lens,  the  greater  the  magnifying  power  of  the  microscope. 
When  great  magnifying  power  is  desired,  it  is  better  to  use 
two  or  more  convex  lenses  combined  so  as  to  act  as  a  sin- 
gle lens  than  a  single  lens  of  greater  curvature. 

Fig.  193- 


258.  The  Compound  Microscope  and  the  Celestial  Tele- 
scope.—  The  combination  of  lenses  employed  in  these  two 
instruments  is  shown  in  Figure  193.  AB  is  the  object; 
i  is  the  objective  lens,  2  is  the  eye-piece,  ab  is  the  image 
formed  by  the  objective,  and  a'  b'  is  the  image  formed  by 


174  ELEMENTS    OF 

the  eye-piece.      The  object  is  beyond  the  focal  length  of 

Fig.  194. 


the  objective.     The  first  image  is  real,  inverted,  and  either 
larger  or  smaller  than  the  object  according  to  the  distance  of 
Fi    j  the  object.     The  rays  which 

meet  at  every  point  of  the 
first  image  cross  and  diverge 
in  front  of  the  image  as  from 
an  object.  The  eye-piece  is 
a  simple  microscope  for  ex- 
amining this  image  as  if  it 
were  an  object.  The  image 
formed  by  the  eye-piece  is  vir- 
tual, erect  as  compared  with 
the  first  image,  and  larger 
than  that  image.  It  is  in- 
verted, as  compared  with  the 
object,  and  whether  larger 
or  smaller  than  the  object  de- 
pends upon  the  size  of  the 
first  image  compared  with 
that  of  the  object. 

A  telescope  is  an  instrument 
for  examining  distant  objects. 
With  the  telescope  they?rj/ 
image  is  smaller  than  the  object,  and  increases  in  size  with 


NATURAL    PHILOSOPHY.  175 

the  focal  length  of  the  objective.  Hence  for  powerful  tele- 
scopes the  objective  is  ground  flat,  so  as  to  have  as  great 
focal  length  as-  possible,  and  made  as  large  as  possible, 
to  admit  the  greatest  possible  amount  of  light. 

The  largest  objectives  now  made  are  from  26  to  30  inches  in 
diameter,  with  a  focal  length  of  from  30  to  40  feet.  They  are 
made  achromatic. 

A  microscope  is  an  instrument/0r  examining  minute  ob- 
jects. The  object,  being  under  our  control,  can  be  placed 
as  near  the  lens  as  we  please,  and  hence  \htfirst  image 
will  be  larger  than  the  object,  and  the  less  the  focal  length 
of  the  objective  the  larger  the  image.  Hence,  for  a  power- 
ful 'microscope,  the  objective  is  made  of  as  short  a  focal 
length  as  possible,  and  since  it  curves  very  rapidly  it  must 
be  very  small. 

The  objective  and  eye-piece  of  the  telescope  and  microscope 
are  mounted  in  a  tube  (Figures  194  and  195).  The  eye-piece  is 
movable,  and  adjusted  so  that  the  final  image  is  about  10  inches 
from  the  eye,  the  point  of  most  distinct  vision. 

259.  The  Terrestrial  Telescope.  —  In  the  celestial  tele- 
scope objects  are  always  seen  inverted  ;  but  this  causes  no 
inconvenience  in  observing  the  heavenly  bodies.  To  make 
terrestrial  objects  appear  erect,  a  second  objective  is  used 

Fig.  196. 


to  invert  the  image  formed  by  the  first  (Figure  196).  AJ3\s 
the  object;  ab  the  image  formed  by  the  first  objec- 
tive, which  falls  without  the  focal  length  of  the  second 
objective ;  and  a'  b'  that  formed  by  the  second  objective. 

260.   The   Opera-Glass.  —  The   objective    of   an    opera- 
glass  is  a  convex  lens,  like  that  of  the  ordinary  telescope, 


i76 


ELEMENTS    OF 


but  the  eye-piece  is  a  concave  lens.  This  lens  is  placed  so 
that  the  real  image  of  the  objective  would  fall  beyond  it 
and  outside  of  its  principal  focus  (Figure  197).  A  B  is 

Fig.  197. 


the  object ;  i  the  objective,  2  the  eye-piece,  a  b  the  image 
that  would  be  formed  by  the  objective  alone,  and  a!  b'  the 
image  formed  by  the  eye-piece.  The  rays  which  meet  the 
eye-piece  from  the  objective  are  converging  to  points  be- 
tween a  and  b.  The  final  image  a'  b1  is  virtual,  erect,  and 
larger  than  the  first  image  would  have  been.  The  two 
tubes  of  an  opera-glass  are  exactly  alike.  They  are  used 
because  it  is  less  fatiguing  to  use  both  eyes  than  only 
one. 

261.  The  Reflecting  Telescope.  —  In  reflecting  telescopes 
the  place  of  .an  object-glass  is  supplied  by  a  concave  mirror, 
called  a  speculum,  usually  composed  of  solid  metal.  The 
real  and  inverted  image  which  it  forms  of  distant  objects  is, 

Fig.  198. 


in  the  Herschelian  telescope,  viewed  directly  through  an 
eye-piece,  the  back  of  the  observer  being  towards  the  ob- 
ject and  his  face  towards  the  speculum  (Figure  198). 


NATURAL    PHILOSOPHY. 


177 


262.  The  Camera  Obscura.  —  The  camera  obscura  is  a 
dark  chamber  having  a  movable  screen  within  it,  and  a 
convex  lens  fitted  into  an  opening  in  front.  This  lens 
forms  a  real  inverted  image  of  the  objects  in  front,  which 
is  received  upon  the  screen. 

In  order  to  receive  the  image  on  a  horizontal  table,  a  lens  of 
the  form  shown  in  Figure  199  is  sometimes  used  at  the  top  of 
the  camera.  The  rays  from  external  objects 
are  first  refracted  at  the  convex  surface,  then 
totally  reflected  at  the  back  of  the  lens,  which 
is  plane,  and  finally  emerge  through  the  bot- 
tom of  the  lens,  which  is  concave,  but  with 
a  larger  radius  of  curvature  than  the  first 
surface. 

The  camera  obscura  employed  by  photog- 
raphers (Figure  200)  is  a  box  J/7V,  with  a 
tube  A  B  in  front,  containing  an  object-glass 
at  its  extremity.  The  object-glass  is  usually 
compound,  consisting  of  two  single  lenses 
EL.  At  G  is  a  slide  of  ground  glass,  on  which  the  image  of 
the  scene  to  be  depicted  is  thrown,  in  setting  the  instrument. 
The  focusing  is  performed  in  the 
first  place  by  sliding  the  part  M  of 
the  box  in  the  part  /V,  and  finally  by 
the  pinion  V,  which  moves  the  lens. 
When  the  image  has  thus  been  ren- 
dered as  sharp  as  possible,  the  sen- 
sitized plate  is  substituted  for  the 
ground  glass. 

263 .  The  Lantern  for  Projection . 
—  The  lantern  is  now  extensively 
used  by  teachers  and  lecturers  for 
projecting  experiments,  diagrams, 
and  views  of  various  kinds  upon  the 
screen.  This  lantern  is  a  kind  of 
reversed  camera.  Some  intense  arti- 
ficial light,  as  the  lime  light  or  the 
electric  light,  is  enclosed  in  an 

12 


178  ELEMENTS    OF 

opaque  box.  A  convex  lens,  called  the  condenser,  fixed  in  an 
opening  in  the  front  of  the  box,  condenses  the  light  upon  the 
transparent  picture  or  object  to  be  projected.  In  front  of  this 
object  is  a  tube  containing  a  combination  of  lenses  exactly  like 
those  used  with  the  camera.  These  form  a  real  inverted  image 
of  the  object  on  the  distant  screen. 

264.  The  Eye.  —  The  human  eye  (Figure  201)  is  a  nearly 
spherical  ball,  capable  of  turning  in  any  direction  in  its  socket. 
Its  outermost  coat  is  thick  and  horny,  and  is  opaque  except  in 
front.  The  opaque  portion  H  is  called  the  sclerotic  coat,  or  the 
white  of  the  eye.  The  transparent  portion  A  is  called  the 
cornea,  and  has  the  shape  of  a  very  convex  watch-glass.  Behind 

Fig.  201. 


the  cornea  is  a  diaphragm  D,  called  the  iris.  It  is  colored  and 
opaque,  and  the  circular  aperture  C  in  its  centre  is  called  the 
ptipil.  By  the  action  of  the  involuntary  muscles  of  the  iris,  this 
aperture  is  enlarged  or  contracted  on  exposure  to  darkness  or 
light.  The  color  of  the  iris  is  what  is  referred  to  when  we 
speak  of  the  color  of  a  person's  eyes.  Behind  the  pupil  is  the 
crystalline  lens  E,  which  is  more  convex  at  the  back  than  in 
front.  It  is  built  up  of  layers  or  shells,  increasing  in  density 
inwards ;  this  tends  to  diminish  spherical  aberration.  The 
cavity  B  between  the  cornea  and  the  crystalline  lens  is  called 
the  anterior  chamber,  and  is  filled  with  a  watery  liquid  called 


NATURAL    PHILOSOPHY. 


I79 


Fig.  202. 


the  aqueous  humor.  The  much  larger  cavity  L,  behind  the 
lens,  is  called  the  posterior  chamber,  and  is  filled  with  a  trans- 
parent jelly  called  the  vitreous  humor,  enclosed  in  a  very  thin 
transparent  membrane.  The  posterior  chamber  is  enclosed, 
except  in  front,  by  the  choroid  coat  I,  which  is  saturated  with 
an  intensely  black  and  opaque  mucus,  called  the  black  pigment. 
The  choroid  is  lined,  except  in  its  anterior  portion,  with  another 
membrane  K,  called  the  retina,  which  is  traversed  by  nerve 
filaments  diverging  from  the  optic  nerve  M. 

A  pencil  of  rays  entering  the  eye  from  an  external  point  will 
undergo  a  series  of  refractions,  first  at  the  anterior  surface  of 
the  cornea,  and  afterwards  in  the  successive  layers  of  the  crys- 
talline lens,  all  tending  to  render  them  convergent.  A  real  and 
inverted  image  is  thus  formed  of  any  ex- 
ternal object  to  which  the  eye  is  directed. 
If  this  image  falls  on  the  retina,  the  object 
is  seen;  and  if  the  image  thus  formed  is 
sharp  and  sufficiently  luminous,  the  object 
is  seen  distinctly. 

265.  The  Structure  of  the  Retina.  —  Fig- 
ure 202  represents  a  portion  of  the  retina 
highly  magnified,  since  the  whole  thickness 
of  this  membrane  does  not  exceed  -fa  of 
an  inch.  The  inner  side  a,  which  is  in  con- 
tact with  the  vitreous  humor,  is  lined  with 
what  is  called  the  limiting  membrane.  Ex- 
ternally and  next  to  the  choroid  coat  it  con- 
sists of  a  great  number  of  minute  rod-like 
and  conical  bodies,  e,  arrayed  side  by  side. 
This  is  the  layer  of  rods  and  cones,  and  oc-  <z 
cupies  a  quarter  of  the  whole  thickness  of  the  retina.  From  the 
inner  ends  of  the  rods  and  cones  very  delicate  radial  fibres 
spread  out  to  the  limiting  membrane  ;  d  and  c  are  layers  of 
granules.  The  fibres  of  the  optic  nerve  are  all  spread  out  be- 
tween b  and  a.  At  the  entrance  of  the  nerve  these  fibres  pre- 
dominate, and  the  rods  and  cones  are  wanting.  At  the  centre  of 
the  back  of  the  eye  there  is  a  slight  circular  depression  of  a 
yellowish  hue,  called  the  macula  lutea,  or  yellow  spot.  In  this 
spot  the  cones  are  abundant  without  the  rods  and  nerve  fibres. 


180  ELEMENTS    OF 

266.  The  Action  of  Light  on  the  Optic  Nerve.  —  The  distri- 
bution of  the  nerve  fibres  over  the  front  surface  of  the  retina 
would  seem  to  indicate  that  they  are  directly  acted  upon  by  the 
light ;  but  this  is  not  the  case.     The  fibres  of  the  optic  nerve 
are  in  themselves  as  blind  as  any  other  part  of  the  body.     To 
prove  this  we  have  only  to  close  the  left  eye  and  with  the  right 
look  steadily  at  the  cross  on  this  page,  holding  the  book  ten  or 
twelve  inches  from  the  eye.     The  black  dot  will  be  seen  quite 

Fig.  203. 

+  O 

plainly  as  well  as  the  cross.  Now  move  the  book  slowly  towards 
the  eye,  which  should  be  kept  fixed  on  the  cross.  At  a  certain 
distance  the  dot  will  suddenly  disappear  ;  but  on  bringing  the 
book  still  nearer  it  will  come  into  view  again.  When  the  dot 
disappears  its  image  falls  exactly  upon  the  point  where  the  optic 
nerve  enters  the  eye,  and  where  there  are  no  rods  and  cones, 
but  merely  nerve  fibres.  Again,  the  yellow  spot  is  the  most 
sensitive  part  of  the  retina}  though  it  contains  no  nerve  fibres. 

It  would  appear,  then,  that  the  fibres  of  the  optic  nerve  are 
not  directly  affected  by  the  vibrations  of  the  ether,  but  only 
through  the  rods  and  cones. 

267.  The  Duration  of  the  Impression  on  the  Retina.  —  The 
impression  made  by  light  on  the  retina  does  not  cease  the  in- 
stant the  light  is  removed,  but  lasts  about  an  eighth  of  a  second. 
If  luminous  impressions  are  separated  by  a  less  interval,  they 
appear  continuous.     Thus,  if  a  stick  with  a  spark  of  fire  at  the 
end  is  whirled  round  rapidly,  it  gives  the  impression  of  a  circle 
of  light.     The  spokes  of  a  carriage  wheel  in  rapid  motion  can- 
not be  distinguished. 

The   zoetrope   illustrates   the    same    principle.     It    consists 
Fig.  204.  (Figure   204)  of   a  cylindrical   paper    box 

turning  on  an  upright  axis.  Near  the  top 
of  the  box  is  a  row  of  slits.  The  succes- 
sive positions  which  a  moving  body  as- 
sumes are  represented  in  order  upon  a 
strip  of  paper,  and  this  is  put  within  the 
box,  which  is  then  whirled  round  rapidly. 
If  we  look  at  the  figures  through  the  slits, 
the  successive  positions  come  before  the 


NATURAL    PHILOSOPHY.  l8l 

eye  one  after  another,  and  the  impression  of  each  lasts  till  the 
next  arrives,  so  that  they  all  blend  into  one,  and  the  object 
appears  to  be  really  going  through  the  evolutions  represented. 

268.  Irradiation.  —  When  a  white  or  very  bright  object  is 
seen  against  a  black  ground  it  appears  larger  than  it  really  is, 
while  a  black  object  on  a  white  ground  appears  smaller  than  it 

Fig.  205. 


really  is.  The  two  circles  in  Figure  205  illustrate  this.  The 
black  one  and  the  white  one  have  just  the  same  diameter. 
This  effect  is  called  irradiation.  It  arises  from  the  fact  that 
the  impression  produced  by  a  bright  object  on  the  retina  ex- 
tends beyond  the  outline  of  the  image. 

269.  The   Optical  Axis  and  the    Visual  Angle.  —  A   line 
drawn  from  the  centre  of  the  yellow  spot  through  the  centre 
of  the  pupil  is  called  the  optical  axis.     Wten  we  look  at  any 
object  we  must  turn  the  eye  so  as  to  direct  this  axis  towards  it. 
This  enables  us  to  appreciate  the  direction  of  the  object. 

We  have  seen  (252)  that  the  image  formed  by  a  convex 
lens  is  contained  between  lines  drawn  from  the  extremities 
of  the  object  through  the  centre  of  the  lens.  In  the  case  of 
the  crystalline  lens,  the  angle  contained  between  lines  thus 
drawn  is  called  the  visual  angle  of  the  object,  and  of  course 
measures  the  length  of  the  image  on  the  retina.  All  objects 
which  have  the  same  visual  angle  form  images  of  the  same 
length  on  the  retina. 

270.  Hoiv  we  estimate  the  Size  of  a  Body.  —  The  visual  angle 
gives  us  no  information  as  to  the  real  size  of  a  body  ;  for  this  angle 
(Figure  206)  diminishes  as  the  distance  of  the  body  increases, 
and  bodies  at  different  distances  may  have  the  same  visual  angle, 
though  they  are  not  of  the  same  size.     Thus,  A  B  and  A '  B'  are 


182 


ELEMENTS    OF 


the  same  object ;  but  A f  B' ,  which  is  farther  off,  has  the  smaller 
visual  angle.  Again,  CD  and  A1 B'  have  the  same  visual 
angle,  but  A'  B'  is  the  larger.  We  must,  then,  know  the  dis- 
tance of  a  body  in  order  to  estimate  its  size  ;  but  when  we  know 

Fig.  206. 


this  distance,  we  estimate  its  size  instinctively.  Thus,  a  chair 
at  the  farthest  end  of  the  room  has  a  visual  angle  only  half  as 
large  as  a  chair  at  half  the  distance,  yet  we  cannot  make  it  seem 
smaller  if  we  try.  If  we  are  in  any  way  deceived  as  to  the  dis- 
tance of  an  object,  we  are  also  deceived  as  to  its  size. 

271.   How  we  estimate  the  Distance  of  an  Object.  —  If  we 


.207. 


refer  to  Figure  207,  we  see  that  when  the  eyes  are  directed  to 
a  distant  object,  as  C,  they  are  turned  inward  but  slightly,  while 
they  are  turned  inward  considerably  when  directed  to  the  nearer 
object  D.  The  muscular  effort  we  have  to  make  in  thus  turning 
the  eyes  inward  so  as  to  direct  them  upon  an  object  is  one  of  the 
best  methods  we  have  of  estimating  its  distance. 

We  also  judge  of  the  distance  of  an  object  from  the  distinct- 
ness with  which  we  see  it-  The  more  obscure  it  is,  the  more 
distant  it  seems.  Thus,  objects  seen  in  a  fog  sometimes  appear 
enormously  large.  They  appear  indistinct,  and  we  cannot  rid 
ourselves  of  the  impression  that  they  are  far  off ;  and  hence 


NATURAL    PHILOSOPHY.  183 

they  seem  large,  though  they  may  really  be  small  and  near 
us. 

The  celebrated  "  Spectre  of  the  Brocken,"  seen  among  the 
Hartz  Mountains,  illustrates  the  effect  of  indistinctness  upon  the 
apparent  size  of  an  object.  On  a  certain  ridge,  just  at  sunrise, 
a  gigantic  figure  of  a  man  had  often  been  seen  walking,  and 
extraordinary  stories  were  told  of  him.  About  the  year  1800 
a  French  philosopher  and  a  friend  went  to  watch  the  spectre. 
For  many  mornings  they  looked  for  it  in  vain.  At  last,  how- 
ever, the  monster  was  seen,  but  he  was  not  alone.  He  had  a 
companion,  and,  singularly  enough,  the  pair  aped  all  the  motions 
and  attitudes  of  the  two  observers.  In  fact,  the  spectres  were 
merely  the  shadows  of  the  observers  upon  the  morning  fog, 
which  hovered  over  the  valley  between  the  ridges  ;  and  because 
the  shadows,  though  near,  were  very  faint,  the  figures  seemed 
to  be  distant,  and  like  gigantic  men  walking  on  the  opposite 
ridge. 

When  we  know  the  real  size  of  an  object,  we  judge  of  its  dis- 
tance from  the  visual  angle  ;  but  we  judge  of  the  distance  of 
unknown  objects  mainly  by  comparing  it  with  the  distance  of 
known  objects.  This  is  one  reason  why  the  moon  appears 
larger  near  the  horizon  than  overhead,  though  she  is  really 
nearer  in  the  latter  case.  When  she  is  on  the  horizon,  we  see 
that  she  is  beyond  all  the  objects  on  the  earth  in  that  direction, 
and  therefore  she  seems  farther  off  than  when  overhead,  where 
there  are  no  intervening  objects  to  help  us  to  judge  of  the 
distance. 

272.  Why  Bodies  near  us  appear  Solid.  —  Hold  any  solid 
object,  as  a  book,  about  a  foot  from  the  eyes,  and  look  at  it  first 
with  one  eye,  and  then  with  the  other.  It  will  be  seen  that  the 
two  images  are  not  exactly  alike.  With  the  right  eye  we  can 
see  a  little  mare  of  the  right  side  of  the  object,  and  with  the  left 
eye  a  little  more  of  its  left  side.  The  blending  of  these  two 
pictures  causes  objects  to  appear  solid. 

The  principle  just  stated  explains  the  action  of  the  stereoscope. 
Two  photographs  of  an  object  are  taken  from  slightly  different 
points  of  view,  so  as  to  obtain  pictures  like  those  formed  in  the 
two  eyes.  These  photographs  are  placed  before  the  eyes  in 
such  a  manner  that  each  eye  sees  only  one,  but  both  are  seen  in 


184  ELEMENTS   OF 

the  same  position  (Figure  208).     The  pictures  are  placed  at  A 
and  B ;   the  rays  of  light  from  them  fall  upon  the   lenses  m 
and  «,  and  in    passing   through  them  are  bent   so  that  they 
Fig.  208.  enter  the  eye  as  if  they  came  from  the 

direction  C.  The  lenses  are  portions 
of  a  double-convex  lens,  arranged  as 
shown  in  the  figure. 

273.  Near-sighted  and  Far-sighted 
Eyes. — To  see  an  object  distinctly,  a 
clear  image  of  it  must  be  formed  on  the 
retina.  When  an  object  is  brought 
quite  near  the  eye,  it  becomes  indis- 
tinct, showing  that  the  rays  are  now 
so  divergent  that  the  lens  cannot  bring 
them  to  a  focus  on  the  retina.  The 
nearest  point  at  which  a  distinct  image 
is  formed  upon  the  retina  is  called  the 
near  point  of  vision,  and  the  greatest 
distance  at  which  such  an  image  is 
formed  is  called  the  far  point.  In 
perfectly  formed  eyes  the  near  point  is 
about  3^  inches  from  the  eye,  and  the  far  point  is  infinitely  dis- 
tant. The  distance  of  the  near  and  far  points,  however,  is  not  the 
same  for  all  eyes.  In  some  cases  the  near  point  is  considerably 
less  than  3^  inches  from  the  eye,  while  the  far  point  is  only 
8  or  10  inches  ;  in  other  cases  the  near  point  is  12  inches  from 
the  eye,  and  the  far  point  infinitely  distant.  The  former  are 
called  near-sighted  eyes,  the  \z.\.ter  far-sighted  ones. 

It  was  once  thought  that  near-sightedness-was  due  to  the  too 
great  convexity  of  the  cornea  or  the  crystalling,  lens,  or  of  both, 
and  far-sightedness  to  the  too  slight  convexity  of  the  same  ;  but 
their  real  cause  lies  in  the  shape  of  the  eyeball,  which  in  far- 
sighted  people  is  flattened,  and  in  near-sighted  people  elongated, 
in  the  direction  of  the  axis.  In  Figure  209  the  curve  N  shows 
the  form  of  the  normal  or  perfect  eye,  N'  of  the  far-sighted 
eye,  and  N"  of  the  near-sighted  eye.  The  parallel  rays  A  and 
A  are  brought  to  a  focus  on  the  retina  of  the  normal  eye,  while 
only  the  convergent  rays  A '  and  A '  are  brought  to  a  focus  on 
the  retina  of  the  far-sighted  eye,  and  only  the  divergent  rays  A  " 


NATURAL    PHILOSOPHY.  185 

on  the  retina  of  the  near-sighted  eye.  A  ",  then,  is  the  far 
point  for  the  near-sighted  eye,  since  the  lens  has  now  its  least 
convexity  ;  and  this  point  must  be  within  1 8  or  20  inches,  since 
the  rays  from  an  object  at  a  greater  distance  are  virtually  par- 
allel, and  cannot  be  brought  to  a  focus  on  the  retina.  The  near 

Fig.  209. 


point  must  be  less  than  for  the  normal  eye,  since  the  retina  is 
farther  from  the  lens,  and  therefore  rays  of  greater  divergence 
can  be  brought  to  a  focus  upon  it.  In  the  far-sighted  eye  the 
retina  is  nearer  the  lens  than  in  the  normal  eye  ;  hence  the  near 
point  must  be  farther  away.  While,  then,  the  normal  eye  sees 
distant  objects  distinctly  without  adjustment,  the  far-sighted  eye 
must  adjust  itself  to  see  such  objects. 

The  defect  of  far-sighted  eyes  can  be  in  a  great  measure 
remedied  by  wearing  convex  glasses,  which  help  to  bring  the 
rays  to  a  focus  on  the  retina,  and  thus  diminish  the  distance  of 
the  near  point.  The  defect  of  near-sighted  eyes  can  be  reme- 
died by  the  use  of  concave  glasses,  which  render  parallel  rays 
divergent,  and  thus  increase  the  distance  of  the  far  point. 

274.  Old  Eyes. —  As  the  eye  grows  old  it  loses  its  power  of 
adjusting  itself  for  near  objects,  and  can  see  distinctly  only  dis- 
tant objects.     This  is  quite  a  different  thing  from  far-sighted- 
ness, though,  like  that  defect,  it  can  be  remedied  by  the  use  of 
convex  glasses. 

G.   COLOR. 

275.  The  Three  Fundamental  Qualities  of  Color.  —  The 
three  fundamental  properties  of  color  are  hue,  purity,  and 
brightness. 


i86 


ELEMENTS   OF 


The  hue  of  color  depends  upon  the  length  of  the  luminous 
waves,  and  corresponds  to  pitch  in  sound.  In  the  spectrum 
of  an  incandescent  solid  we  have  all  possible  hues  from 
the  red  through  the  green  to  the  violet. 

By  the  purity  of  a  color  or  hue  we  mean  \\&  freedom  from 
admixture  with  white  light.  Most  natural  and  artificial 
colors  contain  a  greater  or  less  proportion  of  white  light 
blended  with  their  fundamental  hue.  This  gives  the  hue 
a  certain  tint  which  varies  with  the  amount  of  the  light 


The    more  white 


light 


present,   the    paler   the 


present. 
color. 

By  the  brightness  of  a  color  we  mean  the  amount  of  light 
in  it.  If  one  colored  surface  diffuses  twice  as  much  light 
as  another,  its  color  is  said  to  be  twice  as  bright.  When 
a  color  is  at  once  pure  and  bright,  it  is  said  to  be  intense  or 
saturated. 

276.  The   Ideal   Color-Disc.  —  Every   possible   hue    of 
color  would  be  represented  on  a  disc  the  color  of  which 
changed  by  insensible  gradation  from  the  red  through  the 
green  to  the  violet,  and  then  around  through  the  purple 
to  the  red  again.     As  such  a  color  disc  can  have  only  an 
ideal  existence  it  is  called  the  ideal  color-disc. 

277.  The   Color  Chart.  —  If   the  ideal   color-disc  were 
divided  into  ten  equal  sectors,  and  each  sector  colored 


Fig.  210. 


with  its  mean  hue  (the  hue  that 
would  result  from  the  blending  of 
all  the  hues  of  the  sector),  there 
would  be  obtained  the  ten  follow- 
ing colors  ;  red,  orange,  yellow, 
yellowish  green,  green,  bluish  green, 
turquoise  blue,  ultramarine,  violet, 
and  purple.  The  disc  thus  divided 
and  colored  (Figure  210)  is  called 
the  color  chart. 
The  colors  of  opposite  sectors  are  complementary  colors, 


NATURAL    PHILOSOPHY.  187 

that  is,  colors  that  would  produce  white  when  blended.  We 
thus  obtain  the  five  prominent  pairs  of  complementary 
colors,  as  follows  :  — 

Red  and  bluish  green, 

Orange  and  turquoise  blue, 

Yellow  and  ultramarine, 

Yellowish  green  and  violet, 

Green  and  purple. 

If  the  disc  had  been  divided  into  20  equal  sectors,  each  colored 
as  above,  there  would  have  been  produced  10  pairs  of  comple- 
mentary colors  ;  if  into  40  equal  sectors,  20  pairs  ;  and  so  on. 

278.  The  Color  Scale.  —  In  order  to  have  the  change  in 
color  equal  in  passing  from  one  sector  to  the  next  in  every 
part  of  the  disc,  it  is  necessary  to 

make  the  sectors  smaller  in  the 
region  of  the  purple  than  in  that  of 
the  green.  In  Figure  211  the  disc 
is  shown  thus  divided  into  12  un- 
equal sectors,  each  being  colored  as 
before.  The  colors  obtained  are 
vermilion,  orange,  yellow,  yellowish 
green,  green,  bluish  green,  turquoise 
blue*  ultramarine,  bluish  violet,  pur- 
plish violet,  purple,  and  carmine.  This  arrangement  of  the 
disc  is  called  the  color  scale. 

The  colors  which  are  nearest  together  on  the  scale  form  the 
poorest  combinations,  while  those  farthest  apart  form  the  best. 
When  the  colors  are  equally  pure  and  bright,  and  cover  equal 
extents  of  surface,  the  best  possible  combination  that  can  be 
formed  with  any  color  on  the  scale  is  that  formed  with  the  sixth 
color  from  it.  The  two  colors  that  will  under  similar  conditions 
combine  best  with  any  color  are  the  third  colors  on  each  side 
of  that  color  on  the  scale. 

279.  T/ie  Three  Primary  Colors.  —  All  possible  hues  of 
color  can  be  obtained  by  mixing  in  various  proportions  the 


i88 


ELEMENTS   OF 


three  hues,  red,  green,  and  violet.     Hence  these  three  hues 
are  called  the  three  primary  colors. 

By  mixing  the  hues  red  and  green  in  various  proportions, 
all  the  hues  from  red  to  green  can  be  obtained.  In  this  ad- 
mixture the  proportion  of  the  red  must  steadily  decrease  and 
that  of  the  green  increase  in  passing  from  the  red  to  the  green. 
By  a  similar  admixture  of  green  and  violet  we  can  obtain  all 
the  hues  that  lie  between  the  green  and  violet ;  and  of  violet 
and  red,  all  the  hues  of  purple  which  lie  between  the  red  and 
violet  opposite  the  green.  The  three  primary  hues  may  be 
blended  by  means  of  the  apparatus  shown  in  Figure  212. 

Fig.  212. 


Fig.  213. 


Three  colored  discs  of  thick  paper  are  employed  with  it.  One 
of  the  discs  must  be  colored  vermilion  red,  another  emerald 
green,  and  the'third  violet.  Each  disc  has  a  small  hole  in  it  at 
the  centre,  and  is  cut  open  on  one 
side  from  the  margin  to  the  centre. 
Any  two  of  the  discs  may  be  com- 
bined by  slipping  one  of  them  into 
the  other  (Figure  213).  By  turning 
around  the  discs  thus  combined  the 
amount  of  each  disc  exposed  may  be  varied  at  pleasure. 


NATURAL   PHILOSOPHY.  189 

Place  the  red  and  green  discs  thus  combined  upon  the  rotat- 
ing disc,  and  turn  the  crank  rapidly.  The  hues  of  the  exposed 
portions  of  the  two  discs  will  be  blended  in  the  eye  (267),  the 
impression  of  the  color  of  each  disc  remaining  on  the  retina  till 
after  the  other  disc  comes  round  into  its  place.  By  changing 
the  proportions  of  the  surfaces  exposed  by  the  discs,  the  pro- 
portions of  the  two  hues  can  be  varied  at  pleasure.  In  a  simi- 
lar way  green  and  violet  or  red  and  violet  may  be  blended  in 
various  proportions. 

280.  Difference  between  mixing  Hues  and  mixing  Pigments. 
—  Fill  two  glass  tanks  having  parallel  sides,  one  with  a  solution 
of  aniline  yellow,  and  the  other  with  an  ammoniacal  solution  of 
sulphate  of  copper,  and  place  each  in  front  of  a  lantern,  so  as 
to  project  two  colored  discs  on  the  screen.  One  of  these  will 
be  yellow  and  the  other  blue.  Turn  the  lanterns  till  the  two 
colored  discs  overlap  or  coincide.  The  resulting  disc  is  white 
(Figure  214).  In  this  case  the  hues  are  mixed  without  any 
mixture  of  substance. 

Fig.  214. 


Now  mix  the  two  solutions  by  pouring  some  of  each  into. a 
third  cell,  and  place  this  cell  before  one  of  the  lanterns.  The 
disc  on  the  screen  will  be  green.  The  same  result  would  be 
obtained  were  two  cells,  each  containing  one  of  the  solutions, 
placed  in  front  of  one  of  the  lanterns  so  that  the  light  must 
pass  through  both  solutions. 

The  yellow  solution  absorbs  and  quenches  all  the  rays  of  the 
spectrum  above  the  green  ;  and  the  blue  solution,  all  those 
below  the  green.  Green  is  the  only  color  which  is  not  absorbed 


IQO   ,  ELEMENTS   OF 

by  either  substance.  Hence,  when  light  is  allowed  to  pass 
through  both  substances,  either  by  mixing  them  in  one  cell,  or 
by  placing  them  in  separate  cells,  one  in  front  of  the  other,  they 
absorb  and  quench  all  the  colors  except  the  green,  and  therefore 
the  disc  obtained  on  the  screen  is  green.  The  hues  of  two 
colored  substances  are  never  blended  when  the  substances  them- 
selves are  mixed.  One  of  the  substances  always  absorbs  and 
quenches  a  part  of  the  rays  which  escape  from  the  other. 

281.  Co  lor- Blindness. — There    are   many  persons   who 
cannot  see  certain  colors.     Such  persons  are  said  to  be 
color-blind.     Color-blindness  usually  takes  the  form  of  red 
blindness,  though  some  eyes  are  blind  to  green,  and  others 
to  violet. 

A  red-blind  person  can  see  no  difference  in  color  between  a 
ripe  strawberry  and  its  leaf.  His  range  of  hues  is  limited  to 
green  and  blue,  and  the  hues  produced  by  their  combinations. 
Such  a  person  will  make  the  most  absurd  mistakes  in  attempt- 
ing to  match  colors,  mistaking  a  bright  scarlet  for  a  black.  As 
the  danger  signal  is  everywhere  a  red  light,  serious  accidents 
have  occasionally  been  traced  to  color-blindness  in  those  em- 
ployed to  observe  the  signals. 

About  one  male  in  every  twenty-five  is  more  or  less  color- 
blind. Comparatively  few  women  are  color-blind. 

282.  Colors  produced  by  Absorption.  —  Most  of  the  colors 
of  non-luminous   bodies    are    produced    by   absorption.     A 
small  portion  of  the  light  that  falls  upon  the  body  is  dif- 
fused at  the  surface.     The  portion  thus  diffused  enables 
us  to  see  the  surface,  and  is  white  or  the  color  of  the  inci- 
dent light.     A  large  portion  of  the  light  is  diffused  from 
particles  in   the   interior   after  it   has  penetrated  the  sub- 
stance of  the  body  to  a  slight  depth.     A  portion  of  this 
light  is  absorbed  and  quenched  in  its  passage  through  the 
substance  of  the  body.     The  light  which  emerges  from  the 
body  will  be  the  light  which  enters   the  body  minus  that 
which  has  been  quenched  by  absorption.    The  color  of  the 
body  will  be  the  color  which  is  produced  by  the  blending  of 


NATURAL    PHILOSOPHY.  191 

the  hues  which  remain  in  the  light  after  it  has  suffered  ab- 
sorption by  the  body.  It  will  be  the  complement  of  the  color 
absorbed^  the  body  (277). 

Bodies  differ  in  color  because  they  absorb  different  constitu- 
ents of  the  white  light  that  falls  upon  them,  or  else  the  same 
constituents  in  different  proportions.  In  either  case  the  hue  of 
the  light  which  escapes  from  the  body  will  be  different.  A 
painter  does  not  create  colors.  He  simply  prepares  the  surface 
of  his  canvas  so  that  it  shall  destroy  all  the  colors  of  white 
light  which  he  does  not  want.  He  produces  the  hue  he  desires 
by  destroying  its  complement.  Many  bodies  do  not  have  the 
same  color  by  gaslight  as  by  daylight,  Some  of  the  constitu- 
ents of  daylight  are  partially  or  wholly  wanting  in  gaslight. 
Hence  the  constituents  which  remain  after  absorption  are  not 
the  same  in  the  two  cases.  Strictly  speaking,  the  color  does 
not  reside  in  the  body,  but  in  the  light  which  it  diffuses.  A 
body  has  no  color  in  the  dark. 

283.  Phosphorescence  and  Fluorescence.  —  Certain  sub- 
stances, after  exposure  to  sunlight,  will  appear  luminous  for  a 
long  time  in  the  dark,  without  any  signs  of  combustion  or  of 
elevation  of  temperature.  Such  substances  are  said  to  be  phos- 
phorescent. The  sulphides  of  calcium  and  of  barium  possess 
this  property  to  a  remarkable  degree,  and  are  therefore  employed 
in  the  manufacture  of  luminous  paint. 

Fluorescence  is  essentially  the  same  as  phosphorescence. 
The  former  name  is  applied  to  the  phenomenon  observed  while 
the  body  is  actually  exposed  to  the  source  of  light,  and  the  latter 
to  the  phenomenon  observed  after  the  light  from  the  source  is 
cut  off.  Phosphorescence  is,  so  to  speak,  a  kind  of  persistent 
fluorescence.  A  thick  piece  of  uranium  glass,  held  in  the  violet 
or  ultra-violet  portion  of  the  solar  spectrum,  is  filled  to  the 
depth  of  from  y£  to  %  of  an  inch  with  a  faint  nebulous  light. 
A  solution  of  sulphate  of  quinine  exhibits  the  same  effect,  the 
luminosity  in  this  case  being  bluish.  If  the  solar  spectrum  is 
thrown  upon  a  screen  freshly  washed  with  sulphate  of  quinine, 
the  ultra-violet  portion  will  become  visible  by  fluorescence. 


192  ELEMENTS   OF 


V. 

MAGNETISM. 

284.  Magnets.  —  An    iron    ore    was    in    ancient   times 
found  at  Magnesia,  in  Asia  Minor,  which  had  a  peculiar 
property  of  attracting  pieces  of  iron ;  hence  this  property 
has  been  named  magnetism,  and  the  body  possessing  it  is 
called  a  magnet.     A  natural  magnet  is  now  usually  called 
a  lodestone.     It  is  one  of  the  oxides  of  iron,  and  is  very 
abundant  in  nature.     Artificial  magnets  are  bars  of  steel, 
sometimes  straight  and  sometimes  bent  in  the  shape  of  a 
horseshoe. 

285.  The   Poles   of   a   Magnet. —  If    a    bar-magnet    is 
plunged  into  iron  filings  and  withdrawn,  the  filings  will 

Fig.  215.  cling  in   large   quantities  to 

the  ends  of  the  bar  and  leave 
the  middle  bare  (Figure  215). 
If  the  magnet  is  very  thick 
in  proportion  to  its  length, 
the  filings  will  adhere  to  all 
parts  of  it,  but  diminish  in 
quantity  rapidly  towards  the  middle.  The  force  of  the 
magnet  resides  chiefly  at  the  ends,  which  are  called  \hzpoles; 
the  middle  line  of  the  bar,  where  magnetic  force  is  entirely 
wanting,  is  called  the  neutral  line. 

When  a  bar-magnet  is  suspended  so  as  to  turn  freely,  it 
will  take  a  north  and  south  direction,  one  end  always  turn- 
ing towards  the  north  and  the  other  towards  the  south. 


NATURAL  PHILOSOPHV.  193 

The  former  is  called  the  north  or  marked  pole  of  the  mag- 
net, and  the  latter  the  south  or  unmarked  pole. 

If  the  marked  pole  of  a  magnet  is  presented  to  the 
marked  pole  of  another  magnet  which  is  free  to  turn, 
there  is  seen  to  be  repulsion  between  the  poles.  The  same 
is  true  if  the  unmarked  pole  of  one  magnet  is  presented 
to  the  unmarked  pole  of  another.  If  we  present  the 
marked  pole  of  one  magnet  to  the  unmarked  pole  of 
another,  we  see  attraction  between  the  poles.  Like  poles 
of  magnets  repel  each  other,  and  unlike  poles  attract  each 
other. 

If  a  magnet  A  B  (Figure  216)  is  broken  into  any  number  of 
pieces,  each  piece  will  be  a  complete  magnet  with  two  poles,  each 

Fig.  216. 


of  the  strength  of  the  original  poles.  In  each  of  the  pieces  the 
pole  a  to  the  left  is  the  same  as  the  pole  A  at  the  left  end  of 
the  original  magnet,  and  the  pole  b  to  the  right  is  the  same  as 
the  pole  B  of  the  original  bar. 

Fig.  217. 
\\V-\\ • : /#E : I////: '. '•/&'££* : ::::: *££:- .-•  '• .; \ '••>. vA\ '•'I'.V-H/ 


286.  Lines  of  Magnetic  Force.  —  Place  a  sheet  of  drawing- 
paper  stretched  on  a  frame  over  a  bar-magnet,  and  sift 
fine  iron  filings  upon  it.  Tap  the  paper  gently,  and  the 
filings  will  arrange  themselves  in  a  system  of  curved  lines 
(Figure  217).  If  a  horseshoe-magnet  is  held  under  the 

13 


194  ELEMENTS    OF 

paper  with  its  poles  against  the  paper,  the  filings. will  form 
the  system  of  curves  shown  in  Figure  218.  These  curves 
mark  the  lines  along  which  the  magnetic  force  acts,  and  show 
the  direction  and  intensity  of  the  force  at  each  point.  The 


curves  are  nearest  together  about  the  poles  of  the  magnet, 
where  the  magnetism  is  most  intense.  The  space  near  a 
magnet  which  is  pervaded  by  its  force  is  called  the  magnetic 
field. 

287.  Magnetic  Induction.  —  If  a  bar-magnet  is  brought 
near  a  piece  of  soft  iron,  it  develops  magnetism  in  it  by  an 
action  called  induction.  If  iron  filings  are  scattered  over 
the  soft  iron  while  under  the  influence  of  the  magnet,  they 
will  adhere  to  its  ends,  as  shown  in  Figure  219.  The  soft 

Fig.  219. 


. 


. 


iron  will  have  two  poles  and  a  neutral  portion  between 
them.  The  near  end  of  the  soft  iron  will  be  the  opposite 
pole  to  that  of  the  bar  presented  to  it ;  and  the  far  end, 
the  other  pole.  Remove  the  magnet,  and  the  iron  filings 


NATURAL    PHILOSOPHY. 


J95 


fall  off  from  the  piece  of  iron,  showing  that  the  iron  retains 
no  traces  of  magnetism,  or  only  very  slight  ones. 

The  attraction  of  pieces  of  iron  by  a  magnet  is  always  pre- 
ceded by  induction,  the  magnet  developing  in  the  portion  of  the 
iron  nearest  it  a  magnetic  pole 
nulikd  its  own.  Hence  pieces 
of  iron  are  attracted  with  equal 
readiness  by  either  pole  of  a 
magnet.  A  piece  of  iron  which 
has  become  magnetic  by  contact 
with  a  permanent  magnet  may 
attract  a  second  piece  of  iron, 
and  this  a  third,  and  so  on  (Fig- 
ure 220).  A  magnetic  chain 
may  thus  be  formed,  each  com- 
ponent of  which  has  two  mag- 
netic poles.  Each  piece  of  iron 
in  the  filings  which  cling  to  the 
poles  of  a  magnet  becomes  a  magnet  through  induction,  and 
these  pieces  are  held  together  by  their  dissimilar  poles. 

A  piece  of  steel  also  becomes  magnetic  by  induction  when 
acted  upon  by  a  magnet,  but  it  is  not  so  powerfully  magnetized 
as  the  soft  iron.  It  is  harder  to  magnetize  the  steel  than  the 
iron,  but  the  steel  retains  its  magnetic  power  after  the  magnet 
has  been  withdrawn. 

288.  Magnetization  of  Steel  Bars.  —  Permanent  magnets 
are  bars  of  steel.  These  may  be  magnetized  either  by  the 
method  called  magnetization  by  single  touch,  or  by  that  called 
magnetization  by  double  touch. 

In  the  former  method,  the  bar  to  be  magnetized  is  laid 
on  a  board  (Figure  221),  near  one  end  of  which  is  a  stop 
whose  height  is  less  than  Fig.  221. 

the  thickness  of  the  bar. 
The  magnet  is  held  in  a 
sloping  position  and  is 
drawn  over  the  bar  several 
times,  always  in  the  same 


196 


ELEMENTS   OP 


Fig.  222. 


direction  and  with  the  same  end  down.  If  the  marked 
end  of  the  magnet  is  drawn  over  the  bar  from  a  to  d,  the 
end  a  will  become  a  marked  pole.  If  the  magnet  is  drawn 
over  the  bar  in  the  opposite  direction,  or  the  other  pole  of 
the  magnet  is  held  downward,  the  end  b  will  become  the 
marked  pole. 

In  the  method  by  double  touch,  two  magnets  are  held 
one  in  each  hand  with  dissimilar  poles  downward  over  the 
centre  of  the  bar  to  be  magnet- 
ized, as  shown  in  Figure  222. 
They  are  now  drawn  apart  quite 
over  the  ends  of  the  bar,  lifted, 
replaced  at  the  centre,  and  again 
drawn  over  the  ends.  This  pro- 
cess is  repeated  several  times.  The  end  of  the  bar  over 
which  the  unmarked  end  of  the  magnet  has  been  drawn 
will  be  the  marked  pole,  and  vice  versa. 

289.  Compound  Magnets.  —  The  lifting  power  of  a  magnet 
generally  increases  with  its  size,  but  small  magnets  are  usu- 
ally able  to  sustain  a  greater 
multiple  of  their  own  weight 
than  large  ones.  Compound 
magnets  consist  of  a  num- 
ber of  thin  bars  laid  side 
by  side,  with  their  similar 
poles  all  pointing  the  same 
way.  Figure  223  represents 
such  a  compound  magnet 
composed  of  twelve  elemen- 
tary bars,  arranged  in  three 
rows  of  four  bars  each. 
Their  ends  are  inserted  in 
masses  of  soft  iron,  the  ex- 
tremities of  which  constitute 
the  poles  of  the  system. 

Figure  224  represents  a  compound  horse- 
shoe-magnet, whose  poles  N  and  S  support  a 


Fig.  223. 


Fig.  224. 


NATURAL    PHILOSOPHY. 


I97 


keeper  of  soft  iron,  from  which  is  hung  a  bucket  for  holding 
weights.  By  adding  fresh  weights  day  after  day,  the  magnet 
may  be  made  to  carry  a  greater  and  greater  load  ;  but  if  the 
keeper  is  torn  away  from  the  magnet,  the  additional  power  is  in- 
stantly lost,  and  the  magnet  is  able  to  sustain  only  its  original 
load. 

290.  Magnetic  Needles.  —  Any  magnet  suspended  at  the 
centre  so  as  to  turn  freely  is  called  a  magnetic  needle.  The 
needle  may  be  suspended  so  as  to  turn  in  a  horizontal 
plane  (Figure  225)  or  in  a  vertical  plane  (Figure  226). 
The  former  is  called  a  horizontal  needle,  and  the  latter  a 
dipping  needle. 

Fig.  225.  Fig.  226. 


291.  Terrestrial  Magnetism.  —  If  a  steel  bar,  exactly  bal- 
anced in  a  horizontal  position  in  the  frame  shown  in 
Figure  226,  which  is  suspended  by  a  thread,  is  then  mag- 
netized, it  will  no  longer  remain  in  equilibrium  in  any  posi- 
tion in  which  it  may  be  placed,  but  it  will  place  itself  in  a 
particular  vertical  plane,  and  will  take  a  particular  direc- 
tion in  this  plane.  The  needle  takes  this  position  in  obe- 
dience to  the  force  of  terrestrial  magnetism.  The  earth  acts 
upon  the  needle  as  if  it  were  itself  a  magnet. 

The  vertical  plane  of  the  needle  is  called  the  magnetic 
meridian.  This  plane  usually  lies  several  degrees  from 


198 


ELEMENTS    OF 


a  north  and  south  direction.     The  difference  between  true 
and  magnetic  north,  or  the  angle  between  the  geographical 

Fig.  227. 


Fig.  228. 


and  the  magnetic  meridian,  is  called  the  declination.  The 
direction  of  the  needle  in  the  vertical  plane  is  seldom  hori- 
zontal, but  inclined  more  or  less  to  the  horizon.  The  angle 


NATURAL    PHILOSOPHY. 


I99 


which  the  needle  makes  with  the  horizon  is  called  the 
dip.  Both  the  declination  and  the  dip  of  the  magnetic 
needle  are  very  different  in  different  parts  of  the  earth. 
As  a  rule,  the  north  pole  of  the  needle  dips  at  places  north 
of  the  equator,  and  the  south  pole  at  places  south  of 
the  equator.  In  the  neighborhood  of  the  equator  there 
is  a  line  around  the  earth  on  which  neither  pole  dips.  This 
line  is  called  the  magnetic  equator.  The  dip  increases  as 
we  proceed  north  and  south  from  the  magnetic  equator. 
The  magnetic  meridians  and  lines  of  equal  clip  are  shown 
in  Figures  227  and  228.  It  will  be  seen  that  the  magnetic 
poles  are  at  some  distance  from  the  geographic  poles.  The 
magnetic  pole  north  of  the  equator  is  a  south  magnetic 
pole,  and  vice  versa. 

Fig.  229. 


292.    The  Mariners  Compass.  —  The  mariner's  compass  is  a 
declination  compass  used  in  guiding  the  course  of  a  ship.     Fig- 
ure 229  represents  a  view  of  Fig.  230. 
the   whole,  and  Figure  230  a 
vertical    section.      It  consists    f 
of    a  cylindrical   case,   B  B', 
which,  to   keep  the   compass 
in  a  horizontal  position  in  spite  of  the  rolling  of  the  vessel,  is 
supported  on  gimbals.      These  are  two  concentric  rings,  one 


t 


200 


ELEMENTS   OF 


of  which,  attached  to  the  case  itself,  moves  about  the  axis 
x  d,  which  plays  in  the  outer  ring  A  /  and  this  moves  in  the 
supports  P  Q,  about  the  axis  m  n,  at  right  angles  to  the 
first.  In  the  bottom  of  the  box  is  a  pivot,  on  which  is  placed 

a  magnetic  bar  ab,  which  is  the 
needle  of  the  compass.  On  this 
is  fixed  a  disc  of  mica,  a  little 
larger  in  diameter  than  the 
length  of  the  needle,  on  which 
is  traced  a  star  with  thirty-two 
branches,  making  the  points  of 
the  compass  (Figure  231).  The 
branch  ending  in  a  small  star 
(Figure  229),  and  marked  A7",  is 
in  a  line  with  the  bar  a  £  (Figure 
230),  which  is  underneath  the 
cisc.  The  compass  is  placed  near  the  stern  of  the  vessel,  in 
sight  of  the  helmsman. 


NATURAL   PHILOSOPHY.  2OI 


VI. 

ELECTRICITY. 

•/• 

FRICTIONAL  ELECTRICITY. 
A.   ELECTRICAL  ATTRACTIONS  AND  REPULSIONS. 

293.  Electrical  Excitation.  —  If  a  dry  stick  of  sealing- 
wax  is  rubbed  with  a  piece  of  dry  flannel,  or  a  vulcanite 
tube  with  a  piece  of  dry  fur,  it  acquires  the  power  of  at- 
tracting light  bodies,  such  as  bits  of  paper,  pieces  of  straw, 
pith  balls,  etc.  The  body  rubbed  is  said  to  be  electrified, 
and  the  force  which  it  manifests  is  called  electricity.  Elec- 
tricity is  developed  whenever  any  two  unlike  bodies  are  rubbed 
together,  though  some  bodies  become  electrified  much  more 
readily  than  others.  The  ancients  noticed  that  amber, 
which  the  Greeks  called  electron,  acquired  the  power  of 
attracting  light  bodies  when  rubbed  ;  hence  the  terms  elec- 
trified and  electricity. 

Electricity  can  be  most  readily  and  conveniently  excited  by 
rubbing  a  smooth  vulcanite  tube,  18  inches  or  so  in  length  and 
%  of  an  inch  in  diameter,  with  a  cat-skin  ;  or  a  glass  tube  of  tht 
same  dimensions  with  a  silk  pad,  composed  of  three  or  four 
layers  of  silk,  and  8  or  10  inches  square.  The  silk  pad  is  much 
more  effective  when  covered  with  amalgam,  a  mixture  of  I 
part  by  weight  of  tin,  2  parts  of  zinc,  and  6  of  mercury.  The 
pad  should  be  first  smeared  with  lard,  and  then  the  powdered 
amalgam  sprinkled  over  it.  The  tubes  and  rubbers  work  best 
when  they  are  dry  and  hot. 


202 


ELEMENTS    OF 


294.  Electrical  Attraction. — A  pith  ball  hung  on  a  silk 
thread  (Figure  232)  will  be  attracted  if  we  present  to  it 
either  an  excited  glass  or  vulcanite  tube,  without  allowing 
it  to  touch  the  ball. 

Fig.  232.  Fig.  233. 


An"  ordinary  walking-stick  placed  in  a  wire  loop,  sus- 
pended by  a  narrow  silk  ribbon  (Figure  233),  may  be 
pulled  around  by  either  of  the  excited  tubes. 

Fig.  234. 


An  ordinary  lath  balanced  on  an  egg  in  an  egg-cup 
(Figure  234)  is  sensibly  attracted  by  the  glass  or  vulcanite 
tube  when  electrified. 

295.  Electrical  Repulsion.  —  Place  an  electrified  glass 
tube  in  the  loop  shown  in  Figure  233,  and  present  another 
excited  glass  tube  to  it.  The  tube  in  the  loop  will  be 


NATURAL    PHILOSOPHY.  203 

repelled.  An  electrified  vulcanite  tube  placed  in  the  same 
loop  will  also  be  repelled  on  presenting  a  second  electrified 
vulcanite  tube  to  it.  If  the  pith  ball  of  Figure  232  is 
allowed  to  touch  either  the  electrified  glass  or  vulcanite 
tube,  it  will  soon  be  repelled,  and  it  cannot  again  be  in- 
duced to  touch  the  tube  (Figure  235). 

296.  Two   Kinds   of  Electricity.  —  If 
an  electrified  vulcanite  tube  is  placed  in 
the  wire  loop  of  Figure  233,  and  an  elec- 
trified glass  tube  is  presented  to  it,  the 
vulcanite  will  be  attracted ;  while,  as  we 
have  seen,  it  will  be  repelled  on  present- 
ing  an   electrified   vulcanite   tube    to    it. 
So,  also,  if  an  excited  glass  tube  is  placed 
in  the  loop,  it  will  be  repelled  by  an  ex- 
cited  glass    tube,    but    attracted    by    an 
excited  vulcanite  tube. 

There  are  thus'/nw  kinds  of  electricity  :  one  appearing  on 
glass  when  rubbed  with  silk,  and  the  other  on  vulcanite  when 
rubbed  with  fur.  The  former  is  called/0.r///z><?,  or  vitreous 
electricity  ;  and  the  latter,  negative,  or  resinous  electricity. 

When  bodies  are  electrified,  they  are  said  to  be  charged 
with  electricity.  Bodies  charged  with  like  electricities  repel 
each  other,  and  those  charged  with  unlike  electricities  attract 
each  other. 

297.  Electrification  of  the  Rubber. — The  silk  pad  used 
in    exciting  the  glass  tube   becomes  negatively  electrified, 
and  the  cat-skin  used  in  exciting  the  vulcanite  becomes 
positively  electrified.     Hang  the  vulcanite  tube  in  the  loop, 
having  first  carefully  discharged  the  tube  by  rubbing  the 
hand  over  it.     Protect  the  silk  pad  from  the  hand  with  a 
piece  of  thin  sheet-rubber.     Excite  the  glass  rod  with  the 
pad,  and  then  present  the  pad  to  the  vulcanite  tube.     It 
will  be  seen   to  attract  the  tube.     Charge  the  vulcanite 
tube  by  friction  with  the  cat-skin,  and  it  will  be  repelled 


204  ELEMENTS    OF 

by  the  pad  which  has  been  used  in  exciting  a  glass  tube, 
showing  that  the  pad  is  negatively  electrified.  Similar 
experiments  may  be  tried  with  the  cat-skin  used  in  exciting 
the  vulcanite  tube.  Whenever  electricity  is  developed  by 
friction,  equal  quantities  of  both  kinds  of  electricity  are  ob- 
tained, one  on  the  body  rubbed  and  one  on  the  rubber. 
i 

B.  ELECTRICAL  CONDUCTION  AND  INSULATIONS 

298.  Cottrelfs  Straw  Electroscope. — An  electroscope  is 
an  instrument  used  for  indicating  the  presence  of  electricity 
and  also  for  ascertaining  whether  the  electricity  is  positive  or 
negative.  The  straw  electroscope,  devised  by  Mr.  Cottrell, 

Fig.  236. 


consists  of  a  small  metallic  disc  M  (Figure  236),  supported 
on  a  rod  of  glass  or  sealing-wax  G,  and  of  a  smaller  disc 
JV,  of  gilt-paper,  above  this,  fastened  with  sealing-wax  to 
one  end  of  a  long  straw  //',  capable  of  turning  upon  the 
needle  a  a  as  an  axis.  The  disc  N  is  balanced  by  a  little 
piece  of  bent  wire  at  /,  just  heavy  enough  to  separate 
N  from  M. 

299.  Conductors.  —  If  a  fine  copper  or  iron  wire  is  fas- 
tened to  the  disc  M  at  one  end,  and  coiled  round  the  glass 
or  vulcanite  tube  at  the  other,  on  exciting  the  tube  the  disc 
N  is  at  once  atracted,  and  the  end  /  of  the  straw  thrown 
upward.  The  attraction  of  the  disc  N  shows  that  the 
electricity  excited  on  the  tube  has  passed  along  the  wire 
to  the  disc  M.  Substances  which  allow  electricity  to  pass 
through  them  are  called  conductors  of  electricity.  The 
metals,  charcoal,  acids,  rain-water,  linen,  plants,  and  ani- 


NATURAL    PHILOSOPHY. 


205 


mals  are  conductors.    Alcohol,  dry  wood,  paper,  and  straw 
are  semi-conductors. 

300.  Insulators.  —  If  the  disc  M  is  connected  with  the 
glass  or  vulcanite  tube  by  means  of  a  silk  thread,  the  disc 
N  will  not  be  attracted  on  exciting  the  tube.     This  shows 
that   electricity  will    not    pass    through  silk.     Substances 
through  which  electricity  will  not  pass  are  called  insulators. 
India-rubber,  vulcanite,  dry  paper,  hair,  silk,  glass,  wax, 
sulphur,  shellac,  and  dry  air  are  insulators. 

Conductors  are  said  to  be  insulated  when  they  are 
completely  surrounded  by  insulators.  A  conductor  may  be 
insulated  by  hanging  it  on  a  silk  cord  or  ribbon,  or  by 
supporting  it  on  glass,  vulcanite,  or  sealing-wax. 

C.  ELECTRICAL  INDUCTION. 

301.  Electrical  Induction.  —  Balance  a  lath  upon  a  warm 
tumbler  or  a  short  rod  of  vulcanite  (Figure  237).     Place 

Fig.  237- 


some  bits  of  paper  or  elder  pith  upon  a  stand  ^4,  three  or 
four  inches  below  the  end  L  of  the  lath,  and  hold  an  ex- 
cited glass  or  vulcanite  tube  near  the  other  end  of  the  lath 
without  touching  it.  The  light  bodies  will  be  attracted, 
showing  that  the  lath  has  been  electrified.  Remove  the 
excited  tube  and  the  light  bodies  will  fall  away,  showing 
that  the  lath  has  again  become  neutralized.  In  this  case 


206  ELEMENTS   OF 

the  electrification  of  the  lath  took  place  through  the  air. 
This  development  of  electricity  by  a  charged  body  through  an 
insulating  medium  is  called  induction. 

302.    The    Electrophorus. —  The    electrophorus    consists 
of  a  plate  of  wax  or  vulcanite  (Figure  238),  and  of  a  licl  of 
Fig.  238.  tin  or  brass  with  an  insulating  handle. 

Excite  the  plate  by  stroking  it  with  a 
cat-skin,  and  place  the  lid  upon  it. 
Owing  to  the  unevenness  of  the  plate, 
the  lid  will  touch  it  at  comparatively 
few  points,  but  the  plate  will  act  upon 
the  lid  by  induction.  Remove  the  lid, 
and  test  it  with  a  suspended  pith  ball 
(Figure  232).  It  shows  no  signs  of 
electrification.  Replace  the  lid  and  touch  it  with  the 
finger.  Remove  the  finger  and  then  the  lid,  and  present 
the  lid  to  the  pith  ball.  The  ball  is  attracted,  showing 
that  the  lid  is  charged.  Allow  the  pith  ball  to  touch  the 
lid.  It  is  immediately  repelled,  having  by  contact  become 
charged  with  the  same  kind  of  electricity  as  that  on  the 
lid.  Present  now  the  plate  of  the  electrophorus  to  the 
charged  pith  ball,  and  the  ball  will  be  attracted,  showing 
that  the  lid  was  charged  with  the  opposite  electricity  to 
that  on  the  plate.  Bodies  charged  by  contact  are  always 
charged  with  the  same  electricity  as  that  on  the  body  acting 
upon  them,  while  bodies  charged  by  induction  are  always 
charged  with  the  opposite  electricity  to  that  on  the  body  acting 
upon  them.  The  lid  of  the  electrophorus  may  be  charged 
any  number  of  times  by  the  plate  without  renewing  the 
charge  on  the  plate. 

3  03 .  The  Gold-Leaf  Electroscope.  —  This  in  strum  e  n  t  (  Fig- 
ure  239)  consists  of  two  strips  of  gold-leaf,  hung  together 
by  their  upper  ends  to  a  metal  rod,  which  passes  through 
a  hole  in  the  top  of  a  glass  globe.  The  rod  terminates 
above  in  a  brass  disc  or  a  brass  ball.  The  glass  insulates 


NATURAL    PHILOSOPHY. 


207 


the  disc  and  leaves,  and  protects  the  leaves  from  currents 
of  air. 

When  an  electrified  body  is  Fie-  239- 

placed  in  contact  with  the 
disc,  it  charges  the  disc  and 
leaves  with  its  own  electricity, 
and  causes  the  leaves  to  di- 
verge (296). 

To  detect  the  kind  of  elec- 
tricity on  the  charged  body,  first 
charge  the  leaves  with  a  known 
kind  of  electricity,  and  then  place 
the  body  to  be  tested  in  contact 
with  the  disc.  If  the  leaves 
diverge  more  than  before,  the 
body  is  charged  with  the  same 
kind  of  electricity  as  that  on 
the  leaves  ;  if  the  leaves  diverge  J 
less  than  before,  the  body  is  ! 
charged  with  the  opposite  elec- 
tricity to  that  on  the  leaves. 

If  a  charged  body  is  brought  near  the  disc  without  touching 
it,  the  leaves  will  diverge,  being  electrified  by  induction.  Re- 
move the  charged  body,  and  the  leaves  come  together  again. 
If  we  present  the  charged  body  again,  and  touch  the  disc  with 
the  finger,  the  leaves  fall  together.  Remove  first  the  finger  and 
then  the  charged  body,  and  the  leaves  again  diverge,  being 
charged  by  induction  with  the  opposite  electricity  to  that  on  the 
charged  body. 

304.  Two  Kinds  of  Electricity  developed  in  Induction.— 
Both  kinds  of  electricity  are  always  developed  in  induction  ; 
the  same  kind  as  that  on  the  inducing  body  being  driven  to 
the  far  end  of  the  conductor,  and  the  opposite  kind  being 
held  on  the  near  end  of  the  conductor. 

Charge  the  lid  of  the  electrophorus,  and  hold  it  near  one  end 
of  an  insulated  conductor  (Figure  240).  Place  the  carrier 
(a  small  metallic  disc  with  an  insulating  handle)  in  contact 


2o8  ELEMENTS    OF 

with  the  lid,  and  then  with  the  disc  of  the  gold-leaf  electro- 
scope, so  as  to  charge  the  leaves  with  the  electricity  on  the 
lid.  Discharge  the  carrier,  and  bring  it  in  contact  with  the 
far  end  of  the  insulated  conductor.  Again  place  the  carrier 
on  the  disc  of  the  electroscope ;  the  leaves  will  diverge  more 

Fig.  240. 


c 


than  before,  showing  that  the  far  end  of  the  conductor  has  upon 
it  the  same  electricity  as  the  inducing  lid.  Again  discharge  the 
carrier,  and  bring  it  in  contact  with  the  near  end  of  the  con- 
ductor. Remove  the  carrier  again  to  the  disc  of  the  electro- 
scope ;  the  leaves  will  diverge  less  than  before,  showing  that 
the  near  end  of  the  conductor  has  the  opposite  kind  of  electricity 
to  that  on  the  lid.  In  a  similar  way  the  centre  of  the  conductor 
will  be  found  to  be  neutral. 

While  the  opposite  electricity  to  that  on  the  inducing  body 
is  held  fast  by  the  inducing  body,  the  other  electricity  is  driven 
off  to  the  farthest  possible  point.  If  two  insulated  conductors 
are  connected  by  a  long  wire,  and  the  lid  of  the  electrophorus 
is  presented  to  one  of  them,  the  near  conductor  becomes 
charged  with  negative  electricity  and  the  far  conductor  with 
positive  electricity.  If  we  touch  a  conductor  under  the  influence 
of  a  charged  body,  or  connect  the  conductor  in  any  way  with  the 
earth,  the  far  end  of  the  conductor  becomes  the  opposite  side 
of  the  earth,  to  which  the  electricity  like  that  on  the  inducing 
body  is  driven.  Hence,  when  bodies  connected  with  the  earth 
are  acted  on  by  induction,  they  have  only  one  kind  of  electricity 
on  them,  and  that  the  opposite  to  that  on  the  inducing  body. 
In  charging  a  conductor  by  induction  we  must  remove  the  earth 
connection  before  removing  the  inducing  body,  else  the  electricity 
which  was  held  fast  on  the  conductor  would  escape  to  the  earth 
to  join  the  electricity  which  had  been  driven  there  before  it. 

305.  Dielectrics.  —  Induction  will  take  place  through  all 
insulating  substances.  When  an  excited  tube  is  brought 
near  the  disc  of  the  electroscope,  the  leaves  diverge  be- 


NATURAL    PHILOSOPHY.  209 

cause  of  the  induction  which  takes  place  through  the  air. 
If  a  plate  of  glass,  of  vulcanite,  of  paraffine,  or  of  shellac, 
is  held  between  the  tube  and  the  disc,  the  leaves  will  still 
diverge  because  of  the  induction  which  is  taking  place 
through  the  plate.  The  substance  through  which  induction 
takes  place  is  called  a  dielectric.  All  insulators  are  dielec- 
trics. 

If  a  metallic  plate,  so  large  that  induction  will  not  take  place 
around  it,  is  held  between  the  tube  and  the  disc  of  the  electro- 
scope, so  as  to  be  in  connection  with  the  earth,  the  leaves  of 
the  electroscope  will  no  longer  diverge.  No  induction  will 
take  place  through  a  conductor.  If  the  conducting  plate  were 
insulated,  induction  would  appear  to  take  place  through  it,  be- 
cause electricity  would  be  developed  on  the  far  side  of  the  plate 
by  induction,  and  this  electricity  would  carry  on  induction 
through  the  air. 

306.  Attraction  and  Repulsion  of  Light  Bodies. — We  now 
see  why  a  charged  body  attracts  a  light  body  not  previously 
charged.     It  first  acts  upon  the  light  body  by  induction,  induc- 
ing a  change  similar  to  its  own  on  the  far  Fig.  241. 

side  of  the  body  and  an  opposite  change 

on  the  near  side  (Figure  241).     The  near 

side  is  attracted  and  the  far  side  repelled ; 

but  the  attracted  side  being  nearer,  the 

attraction  is  stronger  than  the  repulsion, 

and  the  body  as  a  whole  is   attracted. 

On  touching  the  charged  body  it  gives  up  to  it  the  electricity  on 

its  near  side,  and  so  becomes  charged  with  the  same  electricity 

as  that  on  the  charged  body,  and  is  then  repelled. 

D.    ELECTRICAL  POTENTIAL. 

307.  Electrical  Potential.  —  The  term  potential  in  Physics 
means  condition  as  regards  work.     The  potential  of  a  point 
with  respect  to  a  force  is  the  condition  of  the  point  as  re- 
gards work.done  by  that  force.    Thus,  the  electrical  potential 
of  a  point  is  its  condition  as  regards  work  done  by  electricity. 

M 


210  ELEMENTS    OF 

Electricity  always  tends  to  move  a  body  charged  with  posi- 
tive electricity  from  a  higher  to  a  lower  potential. 

When  two  points  are  at  the  same  electrical  potential,  elec- 
tricity does  not  tend  to  move  a  charged  body  from  either  point 
to  the  other,  and  consequently  no  work  would  be  done  by  elec- 
tricity upon  a  charged  body  in  its  motion  from  one  point  to  the 
other. 

In  electricity,  the  potential  of  the  earth  is  taken  as  zero,  and 
the  potential  of  a  point  is  really  the  difference  between  its 
potential  and  that  of  the  earth.  Electrical  potential  is  usually 
defined  in  terms  of  positive  electricity.  A  positive  potential  is 
one  higher  than  that  of  the  earth,  and  a  negative  potential  is 
one  lower  than  that  of  the  earth. 

308.  Electrometers.  —  An  electroscope  is  an  instrument  for 
detecting  the  presence  of  electricity,  and   for  ascertaining  its 

Fig  242.  quality.  An  electrometer  is  an  instrument  for 
measuring  the  intensity  of  electrical  attraction  and 
repulsion,  and  for  ascertaining  the  potential  of  a 
body. 

The  pith-ball  electrometer  is  shown  in  Fig- 
ure 242.  A  wooden  stem  C  is  mounted  in  a 
metallic  socket,  which  can  be  screwed  to  the 
conductor  whose  electrification  is  to  be  meas- 
ured. A  pith  ball  fixed  to  a  straw  stem  A  hangs 
from  a  pivot  at  the  centre  of  the  divided  arc  B. 
Electricity  is  communicated  from  the  metal 
socket  to  the  ball,  which  is  repelled.  The  number  of  de- 
grees over  which  the  straw  passes  indicates  roughly  the 
strength  of  the  electrification  of  the  conductor. 

E.    ELECTRICAL  CHARGE  AND  DISCHARGE. 

309.  The  Charge  entirely  on  the  Surface.  —  Suspend  a 
tea-canister  by  a  silk  cord,  and  charge  it  as  highly  as  pos- 
sible by  means   of  the  electrophorus  or  other  electrical 
machine.     Lower  a  brass  ball  hung  on  a  silk  thread  into 


NATURAL    PHILOSOPHY.  211 

it,  so  as  to  touch  the  interior,  and  then  remove  it  without 
touching  the  mouth  of  the  canister.  Test  the  ball  with  an 
electroscope,  and  it  will  be  found  to  have  brought  away  no 
electricity  from  the  can.  Bring  the  ball  in  contact  with 
the  outside  of  the  canister  and  present  it  to  the  electro- 
scope, and  it  will  be  found  to  have  taken  electricity  away 
from  the  canister.  By  no  means  can  any  electricity  be 

found  on   the  inside  of  a  hollow  conductor.     Hence  we 

\ 

conclude  that  the  charge  resides  entirely  on  the  surface ;  un- 
less, of  course,  a  charge  is  developed  on  the  inside  of  the 
hollow  conductor  by  the  induction  of  a  charged  body  sus- 
pended within  it. 

Fig.  243.  Fig.  244. 


310.  Distribution   of  Electricity  over  the  Surface  of  a 
Charged  Body.  —  Were  a  spherical  conductor  suspended 
on  a  silk  thread  in  the  centre  of  a  large  room,  and  charged 
with  electricity,  the  charge  would  be  distributed  uniformly 
over  the  surface,  as  shown  by  the  dotted  line  In   Figure 
243.     The  dotted  lines  in  Figures  244,  245,  and  246  show 
the  distribution  of  electricity  over  the  surface  of  an  ellip- 
soid, a  cylinder  with  rounded  ends,  and  a  disc  under  simi- 
lar circumstances.     When    the   conductor    is   oblong,    the 
electricity  tends  to  accumulate  at  the  ends.     The  longer  and 
thinner  the  conductor,  the  greater  the  accumulation  at  the 
ends. 

311.  Density  of  the  Charge.  —  The  intensity  of  the  elect ri-  ^ 
fication  at  any  point  on  a  body  is  called  the  electric  density 


212  ELEMENTS    OF 

at  that  point.  The  charge  of  a  body  is  the  quantity  of 
electricity  on  it. 

The  force  with  which  electricity  endeavors  to  escape 
from  any  portion  of  surface  increases  with  the  density  at 
that  point.  The  density  on  different  parts  of  the  surface 
depends  upon  the  form  of  the  conductor  and  the  influence 
of  surrounding  bodies. 

Charged  conductors  with  points  attached  to  them  become 
rapidly  discharged  by  the  escape  of  electricity  from  the  point. 
When  points  connected  with  the  earth  are  presented  to 
charged  bodies,  the  bodies  become  rapidly  neutralized  by  the 
escape  of  the  opposite  electricity  from  the  point  to  them. 

312.  J^endency  of  Electricity  to  escape  from  Points.  —  If  a 
sharp  metallic  point  is  fixed  to  one  end  of  a  small  insulated  con- 
ductor, and  the  lid  of  the  electrophorus  charged  with  positive 
electricity  is  held  in  front  of  the  point  so  as  to  act  upon  the 
conductor  by  induction,  negative  electricity  will  escape  from 
the  point  to  the  lid,  and  on  removing  the  lid  the  conductor  will 
be  found  to  be  charged  feebly  with  positive  electricity.  If  the 
charged  lid  of  the  electrophorus  is  held  near  the  other  end  of 
the  conductor,  positive  electricity  will  escape  from  the  point, 
and  on  removing  the  lid  the  conductor  will  be  found  to  be 
charged  feebly  with  negative  electricity.  If  a  plate  of  dry  glass 
is  held  between  the  lid  of  the  electrophorus  and  the  point,  neg- 
ative electricity  will  escape  from  the  point  to  the  glass,  which 
will  be  found  on  examination,  after  removal,  to  be  charged  with 
negative  electricity. 

313.  The  Electrical  Machine.  —  A  common  form  of  this 
machine  is  showrn  in  Figure  247.  A  circular  glass  plate 
supported  by  a  wooden  frame  turns  between  two  pairs  of 
cushions,  one  above  and  the  other  below  the  axis.  In 
front  of  the  plate  are  two  metallic  conductors  supported  on 
glass  legs.  An  arm  studded  with  metallic  points  directed 
towards  the  plate  is  connected  with  each  of  these  conduc- 
tors. The  plate  becomes  charged  with  positive  electricity 
by  friction  as  it  turns  between  the  cushions,  and  acts  upon 


NATURAL    PHILOSOPHY. 


213 


the  points  by  induction.  Negative  electricity  escapes  from 
the  points  to  the  plate,  neutralizing  the  positive  electricity, 
while  positive  electricity  accumulates  on  the  conductors.  The 

Fig.  247. 


Fig.  248. 


cushions  are  connected  with  the  earth  to  allow  the  nega- 
tive electricity  developed  on  them  to  pass  off.  To  avoid 
loss  of  electricity  from  the  portion  of  the  plate  which  is 
passing  from  the  cushions  to 
the  points,  it  is  covered  with 
sectors  of  oiled  silk  on  both 
sides. 

Every  electrical  machine 
may  be  considered  as  a  kind 
of  electrical  pump  for  raising 
electricity  to  a  higher  potential. 
With  the  frictional  machine 
only  a  small  quantity  of  elec- 
tricity is  developed,  but  it  is 
raised  to  an  enormously  high  potential. 

314.    TJie   Electric    Wind.—  The   electricity   which   escapes 


214 


ELEMENTS   OF 


from  a  point  charges  the  molecules  of  air  in  front  of  it,  which 
are  then  repelled  by  the  point.  As  new  molecules  come  in  to 
take  the  place  of  these,  they  are  again  charged  and  repelled.  In 
this  way  a  current  of  air  is  made  to  set  off  from  the  point, 
which  may  be  felt  by  the  hand  or  be  made  to  flare  the  flame 
of  a  candle  if  the  point  is  connected  with  the  conductor  of  an 
electrical  machine  (Figure  248). 

315.  The  Electric  Mill.  —  The  electric  mill  (Figure  249) 
consists  of  a  set  of  metallic  arms  radiating  horizontally  from  a 
centre  which  is  poised  upon  a  point  so  as  to 
turn  freely.  The  arms  are  pointed  at  the 
ends  and  all  bent  around  in  the  same  direc- 
tion. When  the  mill  is  connected  with  the 
conductor  of  an  electrical  machine  in  action, 
the  arms  revolve  in  a  direction  opposite  to 
that  in  which  their  ends  point.  The  motion 
of  the  mill  is  due  to  the  reaction  of  the  mole- 
cules of  the  air  upon  the  points. 

316.  The  Ley  den  Jar. — The  Ley  den 
jar  consists  of  a  wide-mouthed  bottle  of  hard  white  glass 
(Figure  250),  coated  inside  and  out  with  tin-foil,  except  for 
a  few  inches  from  the  mouth.  The  bottle  is  closed  with 
a  lid  of  hard  wood,  in  the  centre  of  which  is  a  brass  rod 
with  a  ball  at  its  top.  A  chain  hangs  from  the  lower  end 
of  the  brass  rocUand  touches  the  inside  tin-foil. 

F'g-  250-  The  inside  foil  can  be  charged  with 

positive  electricity  by  placing  the  ball 
near  the  conductor  of  an  electrical 
machine,  and  working  the  machine  as 
long  as  the  sparks  will  pass.  When 
sparks  refuse  to  pass,  the  inner  foil  is 
charged  almost  to  the  potential  of  the 
conductor  of  the  machine.  This  posi- 
tive charge  acts  inductively  through  the 
glass,  and  induces  a  negative  charge  on 
the  inside  of  the  outer  tin-foil,  and  a 
positive  charge  on  its  outside.  If  the 


NATURAL    PHILOSOPHY. 


2I5 


outer  tin  foil  is  connected  with  the  earth,  the  positive 
electricity  is  driven  off  into  the  earth,  while  the  negative 
electricity  is  held  next  to  the  glass. 

The  jar  may  be  gradually  discharged  by  an  arrangement 
shown  in  Figure  251.  The  rod  connected  with  the  inner 
coating  has  a  bell  upon  the  top  of  it,  while  a  second  bell  on 

Fig.  251. 


a  metallic  rod  is  connected  with  the  outer  coating  by  means 
of  a  strip  of  tin-foil  on  the  base.  A  small  metallic  ball  is 
hung  between  the  bells  on  a  silk  thread.  The  ball  is  first 
attracted  by  the  positive  bell,  and  becomes  charged  with 
positive  electricity.  It  is  then  repelled  to  the  other  bell, 
which  has  become  negative  by  the  release  of  some  of  the 
negative  electricity  on  the  outer  Jin-foil,  owing  to  the  re- 
moval of  some  of  the  positive  electricity  from  the  inner 
tin  coating  of  the  jar.  It  gives  up  its  positive  electricity 
to  this  bell,  and  is  then  again  attracted  to  the  positive 
bell. 

The  jar  may  be  suddenly  discharged  by  means  of  a  dis- 
charging rod,  as  shown  in  Figure  252.  The  outside  coating 
is  touched  with  one  end  of  the  discharging  rod,  and  the 
other  end  is  brought  near  the  ball,  when  the  electricities 


2l6 


ELEMENTS   OF 


combine  with  a  flash  and  a  report.     Immediately  after  this 
has  occurred,  the  jar  is  found  to  be  completely  discharged. 
Fig.  252.  After  a  short  time,  however, 

the  jar  will  be  found  to  have 
acquired  again  a  small  charge. 
This  second  charge  is  called 
the  residual  charge. 

/  'fl  £31  3I7'     The  Holtz  Electrical  Ma- 

chine. —  This  is  one  of  the  most 
powerful  machines  ever  yet  in- 
vented for  obtaining  electricity 
of  high  potential.  In  its  simplest  form  it  consists  of  two  rather 
thin  discs  of  glass  placed  near  together  in  a  vertical  position, 
as  shown  in  Figure  253.  One  of  these  discs  is  capable  of 
turning  rapidly  on  a  horizontal  axis  passing  through  a  hole  in  the 
centre  of  the  other  disc,  which  is  stationary.  The  rotating  disc 
is  a  little  smaller  than  the  other,  and  has  no  openings  in  it. 
There  are  two  apertures,  called  windows,  in  the  stationary  disc 
at  the  ends  of  a  horizontal  diameter.  Just  above  one  of  these 
windows  and  below  the  other,  there  is  a  paper  sector  fixed  upon 
the  disc.  Blunt  tongues  of  paper  run  from  each  sector  through 
the  window  so  as  to  touch  lightly  the  rotating  disc.  In  front  of 

Fig.  253. 


the  rotating  disc  there  is  a  metallic  comb  with  its  points  towards 
the  disc  and  just  in  front  of  the  tongues  from  the  paper  sectors. 
These  combs  are  connected  with  the  discharging  rods,  which 


NATURAL    PHILOSOPHY.  2 17 

constitute  the  poles  of  the  machine.     Under  each  discharging 
rod  is  a  small  Leyden  jar,  or  condenser. 

On  beginning  to  use  the  machine,  it  is  necessary  to  charge 
the  two  paper  sectors,  one  wjth  positive  and  the  other  with  nega- 
tive electricity. 

318.  The  Spark  Discharge.  —  If  we  separate  the  dis- 
charging rods  of  a  Holtz  machine,  and  turn  the  disc  rap- 
idly, a  torrent  of  sparks  will  pass  between  the  rods.  These 
sparks  are  due  to  the  passage  of  electricity  through  the  air 
between  them.  The  spark  is  the  ordinary  form  of  electrical 
discharge  through  dry  gases  of  the  ordinary  density. 

The  spark  is  of  very  short  duration,  lasting  less  than  one 
thousandth  of  a  second.  It  is  very  brilliant,  and  the  im- 
pression of  its  light  lasts  much  longer  than  the  spark 
itself  (267). 

This  may  be  shown  by  the  following  experiment.  A  disc 
(Figure  254)  divided  into  a  number  of  Fig.  254- 

sectors  alternately  black  and  white  is 
put  into  rapid  rotation.  The  colors 
of  the  sectors  blend  in  the  eye  so  that 
they  become  utterly  undistinguishable, 
and  the  disc  appears  of  a  uniform 
gray.  If  the  whirling  disc  is  placed 
in  a  darkened  room  and  illuminated 
by  a  succession  of  electric  sparks, 
each  sector  becomes  perfectly  distinct,  and  the  disc  appears  to 
be  standing  still.  The  disc  is  visible  only  while  the  light  of  the 
spark  is  upon  it,  and  the  duration  of  the  light  is  so  short  that 
the  disc  does  not  have  time  to  turn  an  appreciable  amount  while 
illuminated  by  it. 

The  light  of  the  spark  is  due  to  the  fact  that  the  air  through 
which  the  electricity  passes  is  heated  white-hot  by  the  electric 
discharge.  The  sound of  the  spark  is  due  to  the  sudden  expan- 
sion and  contraction  of  this  heated  air. 

When  the  spark  is  short  it  is  usually  straight.  When  it  is 
long  the  spark  becomes  zigzag  and  branching,  as  shown  in 
Figure  255. 


2l8 


ELEMENTS   OF 


319.  The  Spangled  Pane.  —  If  a  number  of  pieces  of  tin-foil 
are  arranged  on  a  plate  of  glass  a  little  way  apart,  and  an  elec- 
tric discharge  is  allowed  to  pass  through  them,  sparks  will  be 

Fig-  255- 


Fig.  256. 


obtained  at  every  interval  between  the  pieces  of  foil  where  the 

electricity  is  obliged  to  pass  through  the  air. 

Very  pretty  effects  may  be  obtained  by  pasting  a  long  strip 

of  tin-foil  on  a  pane  of  glass  in  parallel  lines  connected  at  alter- 
nate ends,  between  a  knob  at  the 
top  and  at  the  bottom  of  the  pane 
(Figure  256),  and  then  tracing  a 
design  on  the  pane  by  means  of 
a  sharp  point,  which  cuts  through 
the  strips  of  tin-foil  wherever  the 
lines  of  the  pattern  cross  them. 
If  a  discharge  is  allowed  to  pass 
between  the  knobs,  the  design 
comes  out  in  light,  a  spark  being 
produced  wherever  a  strip  of  tin- 
foil is  cut  through.  Such  a  pane 
of  glass  is  called  a  spangled  pane. 
When  the  two  knobs  of  the  pane 
are  connected  with  the  two  dis- 
charging rods  of  a  Holtz  machine 
in  action,  the  effect  is  very  pleasing. 
The  rod  or  wire  from  one  of  the 

knobs  should  not  quite  touch  the  discharging  rod  of  the  machine. 

An  interval  of  half  an  inch  should  be  left  for  sparks  to  pass. 
320.   The  Auroral  Discharge.  —  An  auroral  tube  is  a  long 


NATURAL    PHILOSOPHY.  2  19 

tube  of  glass,  one  or  two  inches  in  diameter,  closed  at  the  ends 
with  brass  caps  through  which  pass  metallic  rods  terminating 
within  the  tube  and  near  its  ends  in  small  brass  balls  or  points. 
One  of  the  caps  is  fitted  with  a  stopcock  for  exhaustion  of  the 
air  from  the  interior.  If  this  tube  is  screwed  to  the  plate  of  an 
air-pump,  and  the  caps  are  connected  with  the  discharging  rods 
of  a  Holtz  machine,  it  will  be  found  that  a  longer  spark  can  be 
obtained  in  a  partial  vacuum  than  in  air  of  the  ordinary  den- 
sity. The  appearance  of  the  discharge  also  changes  as:tthe  ex- 
haustion proceeds.  The  light  becomes  softer  and  more  diffused 
until  finally  the  whole  tube  is  filled  with  a  pale  luminosity.  At 
the  same  time  the  noise  of  the  spark  is  diminished  till  the  dis- 
charge becomes  inaudible. 

This  form  of  discharge,  which  is  common  to  all  highly  rare- 
fied gases,  is  called  the  auroral  discharge,  or  the  vacuum  dis- 
charge. The  color  of  the  light  changes  with  the  gas  used. 

Tubes  containing  various  gases  in  a  highly  rarefied  state  are 
often  prepared  and  sealed  up  so  as  to  be  ready  for  use  without 
the  trouble  of  exhaustion.  These  tubes  are  called  Geissler>s 
tubes,  or  vacuum  tubes. 

The  light  of  the  auroral  discharge  has  great  power  of  'exciting 
fluorescence  (283).  If  any  portion  of  the  glass  of  the  tube  is  col- 
ored with  a  fluorescent  substance,  as  uranium,  or  any  portion  of 
the  tube  passes  through  a  fluorescent  liquid,  as  a  solution  of 
sulphate  of  quinine,  when  the  discharge  takes  place,  the  ura- 
nium glass  glows  with  a  soft  green  light,  and  the  sulphate  of 
quinine  with  a  soft  blue,  each  becoming  fluorescent.  The 
accompanying  plate  represents  a  vacuum  tube.  The  spiral 
portion  near  each  end  passes  through  a  solution  of  sulphate  of 
quinine  contained  in  a  wider  external  tube.  The  green  por- 
tions are  colored  with  uranium.  The  red  shows  the  natural 
color  of  the  discharge  in  rarefied  air.  The  sulphate  of  quinine 
is  quite  colorless  by  ordinary  daylight,  and  the  uranium  very 
nearly  so. 

321.  The  Glow  Discharge.  —  When  a  metallic  point  is 
attached  to  the  conductor  of  an  electrical  machine  in  ac- 
tion, it  wijl  be  seen  in  the  dark  to  be  covered  with  a  soft 
glow  of  light.  A  stream  of  molecules  of  air  sets  off  from 


220  ELEMENTS    OF 

the  point  (314),  carrying  electricity  away  with  them,  and  so 
discharging  the  conductor.  This  discharge  is  called  con- 
vective  discharge.  The  surfaces  between  which  convective 
discharge  is  taking  place  are  covered  with  a  faint  glow  of 
light.  Hence  convective  discharge  is  often  called  glow  dis- 
charge. In  spark  discharge  the  electricity  leaps  from  mole- 
cule to  molecule  through  the  intervening  air,  while  in  convective 
discharge  the  electricity  is  carried  along  by  the  molecules 
which  traverse  the  intervening  space. 

322.  The  Brush  Discharge.  —  Remove  the  condenser 
from  under  the  discharging  rods  of  a  Holtz  machine,  put 
the  machine  in  action,  and  separate  the  rods.  Instead  of 
the  ordinary  spark  discharge  we  shall  find  the  space  be- 
tween the  rods  filled  with  a  pale,  diffused  purplish  light. 
From  the  form  of  this  light,  this  discharge  has  been  called 
the  brush  discharge. 

Fig.  257. 


The  brush  discharge  seems  to  be  a  blending  of  the  spark  and 
the  convective  discharge.     The  electricity  is  some  of  the  time 


NATURAL    PHILOSOPHY.  221 

carried  by  the  molecules  of  the  air,  and  some  of  the  time  it  leaps 
along  from  molecule  to  molecule.  In  a  darkened  room  brushes 
of  light  will  be  seen  on  various  parts  of  a  powerful  Holtz  machine 
in  action.  The  brush  sometimes  assumes  the  form  shown  in 
Figure  257. 

II. 

VOLTAIC  ELECTRICITY. 
A.   DEFLECTION  OF  THE  NEEDLE. 

323.  The    Electric    Current. — The  flow    of   electricity 
through   a   conductor  is    called   the   electric  current.      The 
phenomena  of  electricity  in  motion,  or  of  current  electricity, 
are  usually  classed  together  under  the  head  of  voltaic  elec- 
tricity, to  distinguish  them  from  those  of  electricity  at  rest, 
or   of  frictional    electricity.     The    former   department    of 
electricity  is  sometimes  called  dynamical  electricity,  electro- 
dynamics, or  electro-kinetics ;  and  the  latter,  statical  electricity, 
or  electro-statics. 

324.  The  Action  of  the  Current  on  the  Magnetic  Needle.  — 
Oersted  discovered,  in  1819,  that  a  current  flowing  through 
a  wire  near  a  magnetic  needle  will  deflect  the  needle.     If  the 

Fig.  258.  Fig  259. 


wire  is  held  over  the  needle  (Figure  258),  the  needle  will 
be  deflected  in  one  direction.  If  the  same  wire  is  held 
under  the  needle  (Figure  259),  the  needle  will  be  deflected 
/;/  the  opposite  direction.  If  the  current  is  made  to  flow  in 
the  opposite  direction  through  the  wire  while  over  or  under 
the  needle,  the  needle  will  be  deflected  in  the  opposite  direc- 
tion to  what  it  was  before. 

If  two  currents  flow,  one  over  the  needle  in  one  direction, 
and  one  under  the  needle  in  the  opposite  direction,  they  will 


222 


ELEMENTS    OF 


both  tend  to  turn  the  needle  the  same  way.      In  any  case,  the 
stronger  the  current  the  greater  the  deflection  of  the  needle. 

If  the  wire  conveying  it  is  bent  round  the  needle,  as  in 
Figure  260,  the  current  will  flow  in  opposite  directions  above 
and  below  the  needle.  Hence  both  portions  of  the  current 
will  tend  to  turn  the  needle  the  same  way,  and  the  deflection 
will  be  greater  than  when  the  current  flowed  simply  over 


Fig.  260. 


Fig.  261. 


or  under  the  needle.  If  the  wire  is  carried  a  second  time 
around  the  needle  (Figure  261),  the  deflection  of  the 
needle  will  be  increased,  since  there  will  now  be  two  cur- 
rents above  the  needle  and  two  below  it,  all  tending  to 
turn  the  needle  the  same  way. 

Fig.  262. 


325.  Ampere's  Rule.  — Ampere  has  given  the  following  rule 
for  ascertaining  the  direction  of  the  deflection  of  the  needle  in 
any  case :  Imagine  a  little  swimmer  in  the  electric  current, 
always  swimming  with  the  current,  and  with  his  face  to  the 
needle.  The  north  pole  of  the  needle  will  always  be  deflected 
to  his  left  (Figure  262). 


NATURAL    PHILOSOPHY. 


223 


Fig.  263. 


326.  The  Simple  Galvanometer.  —  A  galvanometer  is  an 
instrument  for  showing  the  presence,  direction,  and  strength 
of  an  electrical  current.     The  simple  galvanometer  consists 
of  a  magnetic  needle,  free  to  turn  in  a  horizontal  or  vertical 
plane,  and  surrounded  with  a  coil  of  wire.     This   galva- 
nometer shows  the  presence  of  a  current  in  the  wire  with 
which  it  is  connected,  by  the  deflection  of  the  needle  ;  the 
direction  of  the  current,  by  the  direction  of  this  deflection ; 
and   the   strength   of   the   current,   by  the  amount  of  the 
deflection. 

327.  The  Astatic  Needle.  —  The  directive  action  of  the  earth 
upon  a  magnetic  needle  impedes  its  deflection  by  the  current. 
This  action  may  be  neutralized  by  com- 
bining two  needles.     The  needles  (Figure 

263)    are    fastened    together    rigidly    at 

the  centre ;  and  the  poles  of  one  needle 

are  the  reverse  of  those   of   the  other. 

As  there  is  a  north  and  a  south  pole  at 

each  end,  each  needle  must  neutralize  the  directive  action  of  the 

earth  upon  the  other.     Such  a  combination  of  needles  is  called 

an  astatic  needle  (unsteady  needle). 

328.  The  Astatic  Galvanometer.  —  An  astatic  galvanometer 
is  one  in  which  an  astatic  needle  is  used.     The  two  needles  of 
the  combination  are  almost,  but  not  quite,  of  the  same  strength. 
They   are    hung    on    a    fibre    of 

silk,  and  the  wire  is  coiled  around 

the    lower   needle    (Figure   264). 

It  will  be  seen  by  Ampere's  rule 

(325)  that  the  current  that  flows 

between  the  needles  will  tend  to 

turn  both  needles  the  same  way, 

while  that  which  flows  under  the 

lower    needle    will   tend   to  turn 

the  needles  in  opposite  directions. 

Owing  to  the  greater  distance,  its 

action  on  the  upper  needle  will  be  much  feebler  than  its  action 

on  the  lower  needle.    Such  a  galvanometer  is  very  sensitive,  since 


224 


ELEMENTS    OF 


Fig.  266. 


the  directive  action  of  the  earth  is  nearly  neutralized,  while  the  ef- 
fective action  of  the  current  is  increased  by  using  two  needles. 

When  it  is  desired  to  make  this  galvanometer  extremely 
sensitive,  the  needles  are 
made  very  light,  and  hung 
on  a  single  fibre  of  silk, 
and  the  wire  is  coiled  sev- 
eral thousand  times  around 
the  lower  needle.  In  this 
case  the  wire  is  very  fine, 
and  is  wound  on  a  flat  reel 
(Figure  265).  The  whole  is 
enclosed  in  a  glass  case,  to 

Fig.  265. 


protect  the  needle  from  currents  of  air  (Figure  266). 

B.    FLOW  OF  ELECTRICITY  THROUGH  CONDUCTORS. 

329.  Electromotive  Force.  —  The  flow  of  electricity  through 
a  wire  connecting  two  conductors  is  analogous  to  the  flow 
of  water  through  a  pipe  connecting  two  reservoirs.  When 
the  water  is  at  the  same  level  in  both  reservoirs,  no  water 
will  flow  through  the  pipe.  When  the  water  is  at  different 
levels  in  the  reservoirs,  it  will  flow  through  the  pipe  from  the 
higher  level  to  the  lower.  The  greater  the  difference  between 
the  levels,  the  greater  the  energy  of  the  current  in  the  pipe. 

In  like  manner,  no  current  of  electricity  will  flow  through 
a  wire  connecting  two  conductors,  when  the  conductors 
are  at  the  same  potential.  When  the  conductors  differ  in 
potential,  a  current  will  flow  through  the  wire  from  the 
higher  potential  to  the  lower.  The  greater  the  difference 
of  potential  between  the  two  conductors,  the  greater  the 
energy  of  the  current. 


NATURAL   PHILOSOPHY.  225 

The  force  which  urges  electricity  through  a  conductor  is 
called  the  electromotive  force.  The  electromotive  force  is 
ahvays  equal  to  the  difference  of  potential  between  the  points 
connected  by  the  wire.  A  certain  standard  electromotive 
force  has  been  selected  as  a  unit,  and  is  called  a  volt.  A 
conductor  designed  to  convey  a  current  is  called  a  circuit. 

330.  Electrical  Resistance.  —  Every    known    substance 
offers   some  resistance  to   the   passage    of    the    current 
through   it,    but   different  substances   differ  greatly   in   the 
amount  of  resistance  which  they  offer. 

The  resistance  of  a  wire  varies  with  its  material,  its 
length,  and  its  thickness.  The  longer  and  thinner  a  wire, 
the  greater  its  resistance.  The  metals  offer  comparatively 
little  resistance  to  the  passage  of  the  current,  and  silver 
the  least  of  them  all.  Copper  stands  next  to  silver.  The 
less  the  resistance  any  substance  offers  to  the  passage  of 
the  current,  the  better  conductor  it  is.  A  certain  standard 
of  resistance  has  been  chosen  as  a  unit,  and  is  called  an 
ohm.  It  is  about  the  resistance  of  250  feet  of  copper  wire 
£<j  of  an  inch  thick. 

331.  The  Quantity  of  the  Current.  —  By  the  quantity  of 
the  current  we  mean  the  amount  of  electricity  flowing  through 
the  circuit  per  second.     The  unit  of  quantity  is  the  amount 
of  electricity  that  a  volt  of  electromotive  force  will  cause  to 
flow  through  an  ohm  of  resistance  in  a  second  of  time.     It  is 

called  a  weber. 

The  pouter  of  a  current  to  deflect  a  needle  is  directly  propor- 
tional to  its  quantity.  Hence  the  quantity,  or  volume,  of  the 
current  is  estimated  by  its  power  of  deflecting  a  needle. 

332.  The  Division  of  the  Current.  —  When  the  circuit  di- 
vides into  two  or  more  branches,  the  current  will  also  divide 
among  the  branches  in  such  a  way  that  the  quantity  of  the  cur- 
rent in  each  branch  will  be  inversely  proportional  to  the  resist- 
ance of  the  branch.     Suppose  the  circuit  divides  at  A  (Figure 
267)  into  four  branches,  W,X,  Y,Z,  whose  resistances  are  in 

15 


226  ELEMENTS    OF 

the  ratio  of  3,  5,  7,  and  9.     Then  ££f  of  the  current  will  pass 
through  W,  jpfg  through  X,  -flfa  through  Y,  and  /T\  through  Z. 


333-  The  Velocity  of  the  Current.  —  The  velocity  of  the  cur- 
rent varies  greatly  under  different  circumstances.  It  ranges  from 
about  13,000  miles  a  second  to  about  60,000  miles  a  second  ;  or 
from  a  velocity  which  would  take  it  around  the  earth  in  two  sec- 
onds to  one  which  would  take  it  twice  around  the  earth  in  less 
than  a  second. 

C.   ELECTRO-CHEMICAL  ACTION. 

7.    VOLTAIC  BATTERIES. 

334.  The   Voltaic  Cell.  —  If  two  metal  plates  Z  and  C 
(Figure  268)  are  partly  immersed  in  a  liquid  which  acts 

Fig  26g  chemically  more  powerfully  upon 

one  of  them  than  upon  the  other, 
and  are  placed  in  metallic  com- 
munication outside  of  the  liquid, 
either  by  direct  contact  or  by 
means  of  a  wire,  a  current  of 
electricity  will  flow  outside  of  the 
liquid  from  the  metal  least  acted 
upon  by  the  liquid  when  alone  to 
the  one  most  acted  upon. 

When  two  metals  are  thus 
arranged  in  a  liquid,  and  are  in  metallic  communication,  the 
one  which,  if  alone,  would  be  least  acted  on,  is  entirely 
protected  by  the  other.  The  arrangement  is  called  a 
voltaic  cell.  The  portion  of  the  plate  least  acted  on,  which  is 
out  of  the  liquid,  is  called  the  positive  pole  of  the  cell,  and 
the  corresponding  part  of  the  other  plate  the  negative  pole. 

335.  The  Zinc  and  Copper  Cell.  —  In  nearly  all  practical 


NATURAL    PHILOSOPHY.  22; 

forms  of  the  voltaic  cell  the  negative  plate  is  zinc.  The 
positive  plate  varies  in  material. 

The  simplest  form  of  the  voltaic  cell  consists  of  a  plate 
of  copper  and  a  plate  of  zinc  partly  immersed  in  dilute  sul- 
phuric acid,  which  acts  on  the  zinc,  but  not  on  the  copper. 
Witji  such  an  arrangement  the  current  ceases  after  a  very 
short  time.  On  examination,  the  copper  will  be  found  to 
be  coated  with  minute  bubbles  of  hydrogen. 

When  a  piece  of  zinc  alone  is  dissolved  in  sulphuric  acid 
diluted  with  water,  it  unites  with  the  acid,  forming  sulphate  of 
zinc,  and  sets  the  hydrogen  of  the  water  free.  When  the  zinc 
is  dissolved  in  the  voltaic  cell,  sulphate  of  zinc  is  formed,  but 
the  hydrogen  is  liberated,  not  at  the  surface  of  the  zinc,  but  at 
that  of  the  copper. 

The  zinc  of  commerce,  of  which  battery  plates  are  made, 
contains  many  particles  of  iron  and  other  metals.  If  a  piece  of 
ordinary  zinc  is  placed  in  acid,  each  of  these  particles  of  iron 
together  with  the  zinc  near  it,  forms  an  independent  small  cell, 
and  the  currents  produced  in  these  small  circuits  cause  the  zinc 
to  be  rapidly  consumed.  The  cost  of  chemically  pure  zinc  pro- 
hibits its  use,  so  a  different  plan  is  used,  which  is  found  to  be 
in  every  respect  equally  efficacious  with  the  employment  of  pure 
zinc.  It  consists  in  coating  the  zinc  with  mercury.  This  is 
done  by  first  immersing  the  zinc  for  a  few  minutes  in  dilute  sul- 
phuric or  hydrochloric  acid,  so  as  to  give  it  a  chemically  clean 
surface,  and  then  pouring  mercury  upon  it.  The  mercury  at 
once  combines  with  the  surface,  and  the  zinc  appears  bright 
like  silver.  Zinc  thus  amalgamated  is  not  attacked  by  dilute 
sulphuric  acid,  unless  it  forms  part  of  a  closed  galvanic  circuit. 

336.  Two-Fluid  Cells.  —  In  all  single-fluid  cells  the 
compounds  formed  by  the  hydrogen  in  the  liquid  which 
absorbs  it  return  to  the  zinc  plate  and  retard  the  action  on 
it.  Cells  with  two  fluids  are  designed  to  prevent  this.  The 
two  principal  types  are  Grove's  and  Daniels  cells.  The 
latter  is  used  when  a  constant  current  of  moderate  strength 
is  required  for  days,  weeks,  or  months ;  the  former,  when 
a  very  powerful  current  is  required  for  a  few  hours. 


228  ELEMENTS    OF 

337.  Grove's  Cell.  —  In  Grove's  cell  the  metals  used 
are  zinc  and  platinum ;  and  the  fluids,  strong  nitric  and 
dilute  sulphuric  acids.  A  cell  of  thin  porous  earthenware 
is  filled  with  nitric  acid,  and  contains  the  platinum  plate. 
This  cell  (Figure  269)  is  placed  within  another  cell  of 
glass  or  vulcanite,  containing  the  zinc  and  dilute  sulphuric 
acid.  The  porous  earthenware,  when  wet,  permits  the 

Fig-  269.  ^         Fig.  270. 


electricity  to  pass  freely  through 
it,  while  it  almost  entirely  pre- 
vents the  mixing  of  the  liquids. 
The  nitric  acid  absorbs  the  hydrogen  as  fast  as  it  is  set  free. 

338.  Bunsen's  Cell.  —  Bunsen's  cell  (Figure  270)  is  simi- 
lar in  construction  to  Grove's,  with  the  exception  that  the 
positive  plate  is  carbon  instead  of  platinum. 

Both  Grove's  and  Bunsen's  cells  give  off  fumes  of  nitrous  acid, 
which  are  unwholesome,  and  injurious  to  instruments.  This  in- 
convenience may  be  obviated  by  using  a  solution  of  bichromate 
of  potash  in  the  porous  cup  instead  of  nitric  acid.  This  arrange- 
ment is  the  two-fluid  bichromate  of  potash  cell.  It  is  much  less 
powerful  than  either  Grove's  or  Bunsen's,  but  is  extensively 
used  for  telegraphic  purposes. 

339.  Darnell's   Cell.  —  In  DanielPs  cell  the   plates  are 
zinc  and  copper.     The  former  is  usually  immersed  in  dilute 
sulphuric  acid,  and  the  latter  in  a  saturated  solution  of  sul- 
phate of  copper. 

A  convenient  form  of  this  cell  is  shown  in  Figure  271.     The 


NATURAL    PHILOSOPHY. 


229 


Fig.  271. 


zinc  in  the  form  of  a  rod  is  placed  inside  the  porous  cell,  which 
is  filled  with  dilute  sulphuric  acid.  The  outer  cell  is  filled  with 
the  solution  of  sulphate  of  copper.  It  is  made  of  copper,  and 
forms  the  positive  plate  of  the  cell. 
Inside  the  copper  cell  and  near  the  top 
is  a  copper  shelf  perforated  with  holes, 
on  which  are  piled  crystals  of  sulphate 
of  copper.  When  the  cell  is  in  action, 
the  hydrogen,  as  it  is  set  free,  is  ab- 
sorbed by  the  solution  of  the  sulphate 
of  copper  which  it  gradually  decom- 
poses. Metallic  copper  is  liberated 
from  this  solution  and  deposited  upon 
the  copper,  while  the  zinc  is  gradually 
consumed  by  the  sulphuric  acid  in  the 
porous  cup.  As  the  solution  of  sul- 
phate of  copper  gets  weaker,  a  fresh 
portion  of  the  sulphate  is  dissolved  from  the  shelf.  The  power 
of  this  cell  steadily  decreases  till  the  dilute  acid  in  the  porous 
cup  is  saturated  with  sulphate  of  zinc,  after  which  it  remains 
constant  for  a  very  long  time.  Fi 

340.  The  Leclanche  Cell.— 
This  consists  of  zinc  and  car- 
bon separated  by  a  porous  cup 
(Figure  272).  The  zinc  is  sur- 
rounded by  a  solution  of  sal- 
ammoniac,  and  the  carbon  by 
a  mixture  of  black  oxide  of  man- 
ganese and  powdered  carbon. 
The  cell  containing  the  powder 
is  filled  up  with  water.  This 
cell  has  small  power,  but  for 
discontinuous  work  will  remain 
in  action  for  years,  without  any 
other  attention  than  occasion- 
ally filling  up  the  cell  with 
water. 


341.   The  Voltaic  Battery.  —  The  voltaic  battery  is  a  combi- 


f- 

230  ELEMENTS    OF 

nation  of  voltaic  cells.  When  the  poles  of  a  cell  are  not 
connected,  they  have  .a  certain  difference  of  potential, 
which  is  nearly  constant  for  each  kind  of  cell,  but  varies 
with  the  different  kinds  of  cells.  When  a  greater  differ- 
ence of  potential  is  required,  it  may  be  obtained  by  con- 
necting a  number  of  similar  cells  in  series,  that  is,  connecting 
the  positive  pole  of  one  cell  with  the  negative  pole  of  the  next ; 
and  so  on.  All  the  poles  are  thus  connected  two  by  two, 
except  in  the  end  cells.  The  free  positive  and  negative 
poles  of  these  two  cells  are  the  positive  and  negative  poles 
of  the  battery. 

The  difference  of  potential  between  the  poles  of  the  battery 
is  as  many  times  that  between  the  poles  of  the  cell  as  there  are 
cells  in  the  battery.  In  a  battery  of  4  cells,  if  we  suppose  the 
difference  of  potential  between  two  poles  of  the  same  cell  to  be 
represented  by  the  number  10,  that  between  the  poles  of  the  bat- 
tery will  be  represented  by  40  ;  if  there  are  five  cells,  by  50 ; 
and  so  on. 

In  electrical  diagrams  a  battery  is  usually  represented  by  a 
series  of  long  and  thin  lines  and  of  short  and  thick  lines.  The 
long  line  at  one  end  represents  the  positive  pole  of  the  battery  ; 
and  the  short  line  at  the  other  end,  the  negative  pole  (Fig- 
ure 273). 

342.  Different  Ways  of  arranging  the  Battery.  —  The 
electromotive  force  of  a  battery  depends  solely  upon  the  number 
of  cells  connected  in  series,  and  not  at  all  upon  the  size  of 
the  plates. 

As  the  electricity  has  to  pass  through  the  battery  as  well  as 
through  the  wire,  the  battery  forms  part  of  the  circuit.  Now  the 
quantity  of  electricity  which  flows  through  a  circuit  depends 
upon  both  the  electromotive  force  and  the  resistance.  The 
greater  the  former  and  the  less  the  latter,  the  greater  the  quan- 
tity of  the  current.  The  larger  the  plates  of  the  cells  the  less 
the  resistance  of  the  battery.  Hence,  with  the  same  number  of 
cells  in  series,  the  larger  the  plates,  the  greater  the  quantity  of 
the  current  which  the  battery  will  give. 


NATURAL    PHILOSOPHY. 


23I 


Instead  of  using  cells  with  larger  plates,  the  cells  are 
usually  connected  side  by  side,  as  shown  in  Figure  274. 
The  effect  of  connecting  cells  side  by  side  is  not  to  increase 
the  electromotive  force  of  the  battery,  but  to  dimmish  its 
resistance,  and  so  to  increase  the  quantity  of  the  current. 

Fig.  273.  Fig-  274. 


In  Figure  275  twenty  cells  are  represented  as  connected  in 
series.  Both  the  electromotive  force  and  the  resistance  of  this 
battery  are  20  times  those  of  a  single  cell  of  the  kind  employed 
in  the  battery. 

Fig.  275. 


•czi 


In  Figure  276  twenty  cells  are  represented  as  connected  side 
by  side.  The  electromotive  force  of  this  battery  is  that  of  one 
cell  only,  but  its  resistance  is  only  ^  of  that  of  one  cell. 

Fig.  276. 


I1_L_L_LJ_11J_1±JL111J_1JJ 
TTTTTT  TTTTTTTTT  TTT 


In  Figure  277  twenty  cells  are  represented  as  connected  in  a 
way  intermediate    between  Fig  277 

the  last   two    cases.     First  \    i    i    t    i 

they  are  arranged  -in  series  >^ 

of  5  each,  forming  4  com-    ^^;;^ 
pound  cells,  which  are  con-  f  ^\^"      \    \    \    \    p 
nected  side  by  side.     The  1  ^.fr   fr   fr    fr 

electromotive   force   of  this    V. 

battery  is  5  times  that  of  a 

single  cell,  and  its  resistance  is  f  that  of  a  single  cell. 


232  ELEMENTS    OF 

II.  ELECTROLYSIS. 

343.  Electrolytic  Action.  —  If  two  platinum  wires,   con- 
nected with  the  poles  of  a  battery  in  action,  are  immersed 
in  dilute  sulphuric  acid,  the  acidwill  be  decomposed.    Hydro 
gen  will  be  set  free  at  the  wire  connected  with  the  negative 
pole  of  the  battery,  while  oxygen  will  appear  at  the  other 
wire.     This  can  be  shown  to  a  class  by  placing  the  dilute 
acid  in  a  tank  with  parallel  glass  sides,  and  throwing  an 
image  of  the  wires  in  the  tank  on  a  screen.     Torrents  of 
bubbles  of  gas  will  be  seen  to  rise  from  the  wires.     The 
decomposition  -of  the  acid  is  the  work  of  the  electric  cur- 
rent, and  is  called  the  electrolytic  action. 

If  a  solution  of  sulphate  of  copper  is  used  instead  of  the 
dilute  sulphuric  acid,  copper  is  deposited  on  the  negative 
wire,  while  oxygen  is  set  free  at  the  positive  wire. 

344.  Faraday's  Nomenclature  of  Electrolysis.  —  Faraday 
called  the  decomposition  of  a  substance  by  means  of  elec- 
tricity, electrolysis ;  the  substance  decomposed,  the  electro- 
lyte; the  poles  at  which  the  decomposition  takes  place,  the 
electrodes ;  the  one  connected  with  the  positive  pole  of  the 
battery  the  anode,  and  the  one  connected  with  the  negative 
pole  of  the  battery  the  cathode;  the  products  of  the  decom- 
position, the  ions ;  the  one  going  to  the  anode  the  anion, 
and  the  one  going  to  the  cathode  the  cation. 

345.  The  Voltameter.  —  The  voltameter  is  an  instrument 
for  measuring  the  quantity  of  the  current.     It  was  invented 
by  Faraday,  and  consists  of  a  dish  filled  with   acidulated 
water  and  fitted  with  electrodes  (Figure  278).     Receivers 
over  the  electrodes  collect  the  gases  as  they  are  set  free. 
The  quantity  of  the  gas  liberated  per  minute  measures  the 
mean  strength  of  the  current  during  the  time,  and  the  total 
quantity  of  the  gas  collected  measures  the  total  quantity  of 
electricity  which  has  passed  through  the  circuit. 

It  is  necessary  to  collect  the  gases  separately,  as  chemically 
clean  platinum  has  the  power  to  cause  the  hydrogen  and  oxy- 


NATURAL    PHILOSOPHY.  233 

gen  to  reunite.  The  receiving  tubes  are  first  filled  with  water 
and  inverted  over  the  electrodes.  As  the  gas  rises  it  displaces 
the  water.  The  receivers  are  graduated  so  as  to  show  the 
amount  of  the  gas  collected. 

Fig.  278. 


346.  Electro-Metallurgy.  —  Whenever  solutions  of  com- 
pounds of  metals  are  decomposed,  the  metal  is  deposited 
upon  the  cathode.     This  deposition  of  metals  by  means  of  the 
electric  current  is  called  electro-metallurgy,  and  is  of  great 
practical  importance.     The  two  chief  processes  of  electro- 
metallurgy are  electrotyping  and  electroplating.     The  former 
is  copying  by  means  of  electricity,  and  the  latter  is  coating 
the  baser  metals  with  the  more  noble  by  means  of  electricity. 

347.  Electrotyping.  —  Anything  may  be  electrotyped  of  which 
a  mould  may  be  taken  in  wax.     The  chief  use  of  electrotyping 
is  in  copying  the  face  of  printers'  type  and  wood-engravings, 
after  they  have  been  arranged  for  the  pages  of  a  book. 

A  mould  is  first  taken  in  wax  of  the  article  to  be  copied,  and 
the  wax  is  coated  with  a  thin  film  of  some  conducting  substance, 
such  as  graphite  powder.  The  mould  is  then  hung  up  in  a  trough 
filled  with  a  solution  of  sulphate  of  copper,  called  the  bath.  The 
mould  is  connected  with  the  negative  pole  of  the  battery,  so  as 
to  make  it  a  cathode.  A  plate  of  copper  is  hung  in  the  bath 
opposite  the  mould,  and  connected  with  the  positive  pole  of  the 
battery,  so  as  to  make  it  an  anode.  On  the  passage  of  the  cur- 
rent through  the  bath,  copper  is  deposited  from  the  solution 
upon  the  mould  in  a  uniform  coherent  sheet,  while  the  anode  is 


234  ELEMENTS    OF 

gradually  eaten  away,  and  keeps  the  bath  of  uniform  strength. 
The  moulds  are  usually  hung  in  the  bath  at  night,  and  in  the 
morning  they  are  removed,  and  the  wax  melted  off.  The  cop- 
per casts  are  made  sufficiently  firm  for  use  in  printing  by  back- 
ing them  with  type-metal. 

348.  Electroplating.  —  The    ordinary   table-ware,    such    as 
knives,  forks,  tea-sets,  etc.,  is  plated  with  silver  by  electrolysis. 
The  article  to  be  plated  is  very  carefully  cleaned,  and  hung  up 
in  a  bath  containing  a  solution  of  cyanide  of  silver.     It  is  then 
connected  with  the  negative  pole  of  a  battery,  while  a  piece  of 
silver  hung  in  front  of  it  is  connected  with  the  positive  pole. 
On  the  passage  of  the  current,  silver  is  deposited  from  the  so- 
lution  upon   the  article  which  forms   the  cathode,  while   the 
silver  of  the  anode  is  gradually  eaten   away,   and  keeps  the 
solution   of  uniform    strength.      If  the   article    is    thoroughly 
cleaned,  and  the  current  is  maintained  at  the  right  strength, 
the  silver  will  be  deposited  uniformly  over  its  surface,  and  will 
adhere  firmly  to  it. 

When  the  article  is  to  be  gilded,  or  coated  with  gold,  the 
bath  must  contain  a  solution  of  the  cyanide  of  gold,  and  the 
anode  must  be  of  gold.  In  other  respects  the  process  is  the 
same  as  in  silver-plating. 

In  nickel-plating  the  bath  contains  a  solution  of  some  com- 
pound of  nickel,  and  the  anode  is  a  piece  of  nickel. 

D.    ELECTRO-MAGNETIC  INDUCTION. 

349.  An  Electric  Whirl  constitutes  a  Magnet.  —  If  a  cur- 
rent of  electricity  is  sent  round  a  wire  bent  in  the  form  of  a 

Fig.  279.         ring  (Figure  279),  the  ring  will  act  in  all  re- 
spects like  a  short  magnet.     The  left-hand  side 
of  the  ring  to  a  person  swimming  round  it 
with  the  current,  and  with  his  face  towards  the 
[j  )]   centre  of  the  ring,  will  be  a  north  pole,  and 

the  other  side  of  the  ring  a  south  pole.  If  the 
wire  is  wound  round  and  round  in  the  form  of 
a  coil,  the  multiplication  of  the  rings  will  produce  a  stronger 
magnet.  By  changing  the  strength  of  the  current  in  such 


NATURAL    PHILOSOPHY.  235 

a  coil,  we  change  the  strength  of  its  magnetism,  and  by 
changing  the  direction  of  the  current  we  reverse  the  poles  of  the 
magnet. 

350.  The  Electro-Magnet.  —  If   a   bar   of    soft   iron   is 
placed    within  the  axis   of    the  coil,  and  a   current   sent 
through  the  coil,  the  iron  becomes  a  magnet,  with  its  north 
pole  to  the  left  hand  of  a  person  swimming  around  the 
coil  with  the  current  and  with  his  face  towards  the  axis  of 
the  coil.     A  wire  coiled  round  a  bar  of  soft  iron  constitutes 
an  electro-magnet. 

Such  a  magnet  is  active  only  while  the  current  is  passing 
through  its  coil.  It  loses  its  magnetism  the  moment  the 
current  stops.  Its  poles  are  reversed  by  reversing  the 
current  in  its  coil.  As  the  strength  of  the  current  increases 
the  magnetism  of  the  magnet  increases,  but  less  and  less 
rapidly,  till  it  reaches  a  certain  point,  beyond  which  an 
increase  in  the  strength  of  the  current  produces  no  increase 
of  magnetism.  At  this  point  the  magnet  is  said  to  be  sat- 
urated. Below  the  point  of  saturation  every  change  in  the 
strength  of  the  current,  however  slight,  produces  a  corre- 
sponding change  of  magnetism. 

Electro-magnets  are  usually  made  of  the  horseshoe  form 
(Figure  280),  and  they  are  much  Fi  2go 

stronger  than  the  ordinary  steel  mag- 
nets. The  iron  core  of  each  coil  is 
often  a  separate  bar,  and  the  two 
bars  are  connected  by  a  straight 
bar  at  the  base. 

35 1.  Magneto- Electric  Currents.  —  If  a  wire  is  moved  in 
the  neighborhood  of  a  magnet  in  any  direction  whatever, 
except  along  a  line  of  magnetic  force,  a  difference  of  poten- 
tial will  be  produced  at  the  ends  of  the  wire  which  would 
cause  a  current  to  flow  through  a  wire  connecting  the  ends 
and  not  acted  on  inductively  by  the  magnet 

If  a  magnetic  pole  is  moved  in  the  neighborhood  of  a 


236 


ELEMENTS   OF 


wire,  in  any  direction  except  parallel  to  it,  a  current  will  be 
induced  in  the  wire.     If,  for  instance,  a  magnet  N S  (Figure 
Fig.  281.  28i)    is   moved   suddenly   in  or 

out  of  the  coil  of  wire,  a  current 
will  be  induced  in  the  coil,  which 
will  be  in  one  direction  on  in- 
serting the  pole,  and  in  the  other 
on  withdrawing  it.  If  the  mag- 
net is  reversed  so  as  to  use  the 
other  pole,  the  current  will  be 
reversed. 

If  a  coil  of  wire  through  which 
a  current  is  passing  is  used  instead  of  a  steel  magnet  (Fig- 
ure 282),  precisely  similar  results  are  obtained.  The  more 
suddenly  the  steel  magnet  or  the  coil  conveying  a  current 
is  moved  in  or  out  of  the  coil,  the  stronger  the  current 
induced. 

Fig.  282.     - 


If  the  small  coil  is  left  within  the  larger  coil,  any  change 
whatever  in  the  current  in  the  inner  coil,  whether  of  strength 
or  direction,  will  develop  a  current  by  induction  in  the  outer 
coil.  So,  too,  if  any  two  coils  of  wire,  through  one  of 
which  a  current  is  passing,  are  near  together,  any  movement 
of  the  coils  with  respect  to  each  other,  or  any  change  in  the 
current  in  the  first,  will  induce  a  current  in  the  second. 

If  a  bar  of  soft  iron  is  inserted  in  the  inner  coil  of  Fig- 


NATURAL    PHILOSOPHY. 


237 


tire  282,  the  current  induced  in-  the  outer  coil,  either  by 
motion  or  change  of  current,  will  be  very  much  stronger. 

Fig.  283. 


352.  The  Bell  Telephone.  —  Figures  283  and  284  show  the 
Bell  telephone,  in  section  and  in  perspective.  It  consists  of  a 
steel  magnet  M  around  one  end  of  Fig.  284. 

which  is  wound  a  coil  of  fine  wire  B. 
The  coil  and  magnet  are  enclosed  in 
a  wooden  case,  which  serves  as  a 
handle.  One  end  of  this  case  is 
enlarged  and  hollowed  out  at  E,  so 
as  to  serve  as  a  mouth-piece  or  an 
ear-piece.  A  diaphragm  of  thin 
iron  D  is  stretched  across  the  wide 
end  of  the  case,  just  in  front  of  the 
pole  of  the  magnet,  which  it  does 
not  touch. 

The  transmitting  and  receiving 
instruments,  which  are  exactly  alike 
in  construction,  are  connected  to- 
gether by  a  wire.  On  speaking 
into  the  mouth-piece,  the  air  in  it  is 
thrown  into  vibration,  and  the  vi- 
brations are  communicated  to  the 
diaphragm.  The  vibrations  of  the 
iron  plate  produce  slight  temporary 
alterations  in  the  magnetism  of  the  steel  magnet.  These 
changes  of  magnetism  in  the  magnet  induce  corresponding  cur- 
rents in  the  wire  of  the  coil,  which  are  transmitted  over  the 
wire  which  connects  the  two  instruments.  Hence  pulsations  of 
electricity  exactly  corresponding  to  the  vibrations  of  the  dia- 


238 


ELEMENTS    OF 


phragm  of  the  first  instrument  will  be  transmitted  over  the  wire 
and  through  the  coil  of  the  receiving  instrument.  These  pulsa- 
tions of  the  current  in  the  coil  will  induce  in  the  magnet  of  the 
receiving  instrument  exactly  the  same  changes  of  magnetism  as 
those  by  which  they  were  produced  in  the  sending  instrument. 
These  changes  of  magnetism  cause  the  magnet  to  pull  upon  the 
iron  plate  in  front  of  it  with  a  varying  force,  and,  consequently, 
to  make  it  vibrate  exactly  like  the  diaphragm  of  the  transmitter. 
These  vibrations  are  communicated  to  the  air,  and  then  to  the 
ear  of  the  operator,  which  is  placed  at  the  mouth  of  the  re- 
ceiver. The  words  spoken  into  the  transmitter  are  thus  repro- 
duced in  the  receiver. 

Figure  285  shows  the  way  in  which  the  two  instruments  are 


X_L\ 


connected.  The  wire  at  each  end  is  connected  with  the  earth 
by  means  of  a  copper  plate  sunk  in  the  ground,  so  that  the  cir- 
cuit is  completed  by  the  earth.  Otherwise  two  wires  must  be 
used  between  the  instruments. 

The  Bell  telephone  is  a  beautiful  illustration  of  electro- 
magnetic induction. 

353.  The  Edison  Telephone. —  In  the  Bell  telephone  no 
battery  is  used.  In  the  Edison  telephone  a  battery  is  used,  and 
a  current  transmitted  from  the  battery  is  thrown  into  undula- 
tions by  an  arrangement  called  the  carbon  button.  In  Figure 
286  b  is  a  disc  or  button  of  carbon,  in  the  form  of  compressed 
lampblack ;  a  and  c  are  metallic  plates  placed  against  the  front 


NATURAL    PHILOSOPHY. 


239 


Fig.  286. 


and  back  of  the  disc.  One  of  the  poles  of  the  battery  B  is 
connected  with  a,  and  the  other  with  c.  The  current  is  obliged 
to  pass  from  the  plate  a  to  c  through  the 
carbon.  An  increase  of  pressure  upon  the 
metallic  plates  a  and  c  diminishes  the  resist- 
ance of  the  button,  either  by  increasing  the 
density  of  the  carbon  or  by  improving  the 
contact  between  the  plates  and  the  disc. 
The  button  is  exceedingly  sensitive  to  varia- 
tions of  pressure,  the  slightest  alteration  of 
pressure  producing  a  change  in  the  strength  of  the  current 
which  traverses  the  carbon. 

One  form  of  the  Edison  transmitter  is  shown  in  Figure  287. 
The  mouth-piece  is  of  vulcanite.     Back  of  this  is  the  vibrating 

Fig.  287. 


disc,  and  behind  this  is  a  little  hemispherical  button  of  alumin- 
ium. This  button  rests  upon  the  metallic  plate  in  front  of  the 
carbon  disc.  This  plate  is  of  platinum.  Behind  the  carbon 
disc  is  a  second  platinum  plate,  held  in  position  by  means  of  the 
screw  at  the  back  of  the  instrument.  The  battery  wires  are 
connected  with  the  two  platinum  plates  in  such  a  way  that  the 
current  must  traverse  the  carbon  disc. 

On  speaking  into  the  mouth-piece,  the  disc  is  thrown  into 
vibration.  The  vibrations  are  communicated  to  the  platinum 
plate  and  the  carbon  disc  by  means  of  the  aluminium  button, 
thus  producing  undulations  in  the  current  exactly  correspond- 
ing to  the  vibrations  of  the  disc. 


240 


ELEMENTS    OF 


The  receiving  instrument  of  the  Edison  telephone  is  similar 
to  that  of  the  Bell  telephone.  Changes  of  magnetism  are  in- 
duced in  it  by  the  undulating  current  which  traverses  its  coil, 
and  these  changes  of  magnetism  cause  the  disc  in  front  of  the 
magnet  to  vibrate  exactly  like  that  of  the  transmitter. 

354.  The  Induction  Coil.  —  The  induction  A?// consists  of 
two  coils:  an  inner  m  primary  coil  of  coarse  wire,  enclos- 
ing pieces  of  soft  iron,  usually  in  the  form  of  wires ;  and 
an  outer  or  secondary  coil  oijine  wire.     The  coils  are  care- 
fully insulated  from  each  other.     A  current  of  electricity 
is   sent  through   the  primary  coil,  and  any  change  in  the 
strength  of  this  primary  current  develops  by  induction  a  cur- 
rent in  the  secondary  coil.    The  induced  current  is  much  less 
in  quantity  (331)  than  the  primary  current,  but  it  has  a  far 
greater  electromotive  force  (329). 

355.  The  Use  of  the  Induction  Coil  with  the  Telephone.  — 
The  induced  currents  from  the  induction  coil  are  better  adapted 

for  working  the  telephone  than 
the  direct  current  from  the  bat- 
tery. Figure  288  shows  the  way 
the  coil  is  used  with  the  tele- 
phone, b  is  the  carbon  disc  of 
the  transmitter,  a  and  c  are  the 
platinum  plates,  B  is  the  battery, 
d  is  the  primary  coil  of  the  in- 
duction coil,  and  ee  its  secondary 
coil.  The  battery  is  connected 
with  the  plates  a  and  c,  and  with 
the  primary  coil  d.  One  end  of  the  wire  of  the  secondary  coil 
is  connected  with  the  earth  by  the  wire  G;  and  the  other  end 
to  the  line  Z,  which  runs  to  the  receiving  instrument.  The  un- 
dulations of  the  current  in  the  primary  coil  induce  correspond- 
ing undulations  of  greater  electromotive  force  in  the  secondary 
coil.  These  latter  undulations  pass  over  the  line,  and  work  the 
receiving  instrument. 

356.  The  Microphone.  —  When  there  is  an  imperfect  contact 
at  any  point  of  a  circuit  carrying  a  battery  current,  any  change 


Fig.  288. 


NATURAL    PHILOSOPHY. 


241 


in  the  quality  of  the  contact  will  produce  a  change  in  the 
strength  of  the  current,  and  cause  a  sound  in  a  telephone  re- 
ceiver included  in  the  (circuit.  When  the  imperfect  contact  is 
between  pieces  of  carbon  lightly  pressed  together,  variations  of 
the  current  are  produced  by  the  slightest  sounds  occurring  near 
the  carbons. 

'  The  microphone  consists  of  three  pieces  of  carbon,  C,  A, 
and  C'  (Figure  289).     The  wires  from  the  battery  B  are  con- 


Fig.  289. 


nected  with  Cand  C'  in  such 

a  way  that  all  the  pieces  of 

carbon    are    in    the   circuit. 

The  wires  X  and    Y  run  to 

the  receiver  of  a  telephone. 

The  lowest  whisper  spoken 

near  the  microphone  is  loudly 

reproduced  in  the  telephone. 

As    the    carbon    rod    A    is 

thrown     into     vibration     by 

the  pulsations   of    sound,  it 

alternately     lengthens      and 

shortens.     These  alterations  of  length  alternately  improve  and 

impair  the  contact  at  C  and  C'. 

Fig.  290. 


To  intensify  the  effect,  the  microphone  is  usually  placed  on 
a  sounding-board  D  (Figure  290).  The  sound  caused  by  a  fly 
walking  on  the  sounding-board  is  distinctly  audible  at  the  dis- 

16 


242  ELEMENTS   OF 

tant  telephone.     The  ticking  of  a  watch  on  the  sounding-board 
sounds  like  the  blows  of  a  hammer. 

357.  Magneto-Electric  Machines.^ —  The  fact  that  electric 
currents  are  produced  in  a  wire  by  any  change  of  mag- 
netism near  it,  or  by  moving  the  wire  in  the  neighborhood 
of  a  magnet,  has  been  utilized  in  the  construction  of  ma- 
chines for  the  development  of  very  powerful  currents  of 
electricity.  These  machines  are  called  magneto-electric  or 
dynamo-electric  machines.  The  former  name  is  applied 
more  especially  to  the  machines  in  which  the  electric  cur- 
rents are  produced  by  changes  of  magnetism,  and  the  latter 
to  those  in  which  the  currents  are  produced  mainly  by  the 
motion  of  wires  in  the  neighborhood  of  magnets.  In  all  the 
dynamo-electric  machines  the  currents  are  produced  by 
revolving  coils  of  wire  between  the  poles  of  powerful 
horseshoe-magnets,  which  are  sometimes  steel  magnets, 
but  usually  electro-magnets. 

Fig.  291. 


E.   TELEGRAPHY. 

358.  The  Principal  Instruments  of  the  Simple  Morse  Tele- 
graph. —  The  principal  instruments  of  the  simple  Morse 
telegraph  are  the  key,  the  relay,  and  the  sounder. 

359.  The  Key.  —  The   key    (Figure    291)    is   used  for 
opening  and  closing  the   circuit.     Its   essential    parts    are 


NATURAL    PHILOSOPHY. 


243 


shown  in  outline  in  Figure  292.  K  is  the  lever  ;  a  is  the 
axis  on  which  it  turns ;  b  is  a  platinum  point  connected 
with  the  lever ;  c  is  a  stationary  platinum  point  directly 
under  b,  called  the  anvil;  and  d  is  a  vulcanite  button  by 
which  the  lever  is  pressed  down.  There  is  a  spring  under 
the  lever  of  the  key  which  keeps  it  up  so  as  to  separate  the 
platinum  points  when  the  lever  is  not  pressed  down. 


Fig.  292. 


K 


293- 


K 


U 


In  Figure  293  the  key  is  shown  in  the  circuit  of  a  bat- 
tery. One  pole  of  the  battery  is  connected  with  the  anvil 
by  a  wire,  and  the  other  with  the  lever  at  the  axis.  When 

Fig.  294. 


the  lever  is  up,  the  circuit  is  opened  at  a  by  the  separation 
of  the  platinum  points,  and  the  current  is  stopped.  When 
the  lever  is  pressed  down,  the  circuit  is  closed  by  the  con- 
tact of  the  platinum  points  at  a,  and  the  current  starts. 


244  ELEMENTS    OF 

360.    The  Sounder.  —  The  sounder  is  shown  in  Figure 

294.     Its   essential  parts  are  shown  in  outline  in  Figure 

Fig.  295.  295.     A  is  an  electro-magnet ;  L 

b        S L  is  a  lever ;  b  is  the  axis  on  which 

the  lever  turns ;  c  is  a  spring 
which  pulls  the  lever  up ;  e  is  a 
piece  of  soft  iron,  fastened  across 
the  lever  just  over  the  electro- 
magnet ;  and  d  is  a  piece  of  metal  against  which  the  lever 
strikes  when  it  is  drawn  down. 

Figure  296  shows  the  sounder  and  key  in  circuit.     One 

Fig.  296. 

K   ~ 


D 


pole  of  the  battery  is  connected  by  a  wire  with  the  circuit 
of  the  key  ;  the  other  pole  is  connected  with  one  end  of 
the  wire  of  the  electro-magnet  of  the  sounder,  and  the 
other  end  of  the  wire  of  this  magnet  is  connected  with 
the  lever  of  the  key  at  the  axis. 

When  the  lever  of  the  key  is  up,  the  circuit  is  broken  at 
a,  the  current  is  stopped,  the  electro-magnet  of  the  sounder 
is  inactive,  and  the  lever  of  the  sounder  is  thrown  up  by 
the  spring.  If  the  lever  of  the  key  is  pushed  down,  con- 
tact is  made  at  a,  which  closes  the  circuit;  the  current 
starts,  the  electro-magnet  of  the  sounder  becomes  active, 
and  the  lever  of  the  sounder  is  drawn  down  by  the  pull  of 
the  magnet  upon  the  iron  above  it.  As  the  lever  is  drawn 
down,  it  clicks  from  striking  the  metallic  stop  at  the  end. 

The  clicking  of  the  sounder  is  controlled  by  the  key, 
even  when  these  are  miles  apart,  for  the  sounder  clicks 
every  time  the  lever  of  the  key  is  depressed.  Letters  and 


NATURAL   PHILOSOPHY. 


245 


words  are  indicated  by  combinations  of  long  and  short  inter- 
vals between  the  clicks.  The  operator  listens  to  the  sounder 
just  as  we  listen  to  one  who  is  talking  to  us,  and  soon 
becomes  able  to  follow  it  as  readily. 

361.    The  Register.  —  Sometimes  an    instrument   called 
the  register  is  used  for  receiving  the  message  instead  of  the 


sounder.  The  essential  parts  of  this  instrument  are  shown 
in  Figure  297.  It  resembles  the  sounder  in  construction 
and  action.  At  the  back  end  of  the  lever  there  is  a  point 
B,  and  just  above  this  point  a  strip  of  paper  C  is  carried 

Fig.  298. 


along  by  clockwork  between  two  rollers  at  Z>.  When  the 
lever  is  drawn  to  the  magnet,  the  point  is  thrown  against 
the  paper  and  scratches  a  line  on  it.  This  line  will  be 
long  or  short  according  to  the  time  the  lever  is  held  down. 


246 


ELEMENTS   OF 


Fig.  299. 


The  long  lines  are  called  dashes  and  the  short  lines  dots. 
These  dots  and  dashes  correspond  to  the  short  and  long 
intervals  between  the  dicks  of  the  sounder,  and  their  combina- 
tions form  the  letters  of  the  alphabet. 

362.  The  Relay.  —  On  long  lines,  in  which  there  are  a  num- 
ber of  stations,  the  current  from  the  main  battery  is  not  strong 
enough  to  work  the  sounders  with  sufficient  force.  This  neces- 
sitates the  use  of  an  instrument  called  the  relay  (Figure  298). 
Its  essential  parts  are  shown  in  outline  in  Figure  299.  A  is 
an  electro-magnet ;  /  is  the  lever,  which 
turns  upon  an  axis  at  b ;  c  is  a  piece  of  soft 
iron  fastened  across  the  lever  in  front  of  the 
electro- magnet;  f  is  a  spring  for  pulling 
the  lever  back  ;  d  and  e  are  two  platinum 
points,  the  former  fastened  to  the  lever  and 
the  latter  stationary. 
Figure  300  shows  the  way  in  which  the  key,  relay,  and 
sounder  are  connected.  The  full  line  represents  the  circuit  of 

Fig.  300. 


K-*- 


'UB. 


the  main  battery  M ;  and  the  dotted  line,  of  the  local  battery  L. 
One  pole  of  the  main  battery  is  connected  with  the  anvil  of  the 
key,  and  the  other  with  one  end  of  the  wire  of  the  electro- 
magnet of  the  relay.  The  other  end  of  the  wire  of  this  magnet 
is  connected  with  the  lever  of  the  key  at  the  axis.  One  pole  of 
the  local  battery  is  connected  to  the  lever  of  the  relay,  and  the 
other  pole  to  the  electro-magnet  of  the  sounder  and  then  to 
the  stationary  platinum  point  of  the  relay.  When  the  lever  of 
the  key  is  up,  the  main  circuit  is  opened  at  a,  the  current  is 
stopped,  the  electro-magnet  of  the  relay  is  inactive,  the  lever 
of  the  relay  is  drawn  back  by  the  spring,  the  local  circuit  is 


NATURAL    PHILOSOPHY.  247 

opened  at£  by  the  separation  of  the  platinum  points,  the  electro- 
magnet of  the  sounder  is  inactive,  and  the  bar  of  the  sounder 
is  thrown  up  by  the  spring.  When  the  lever  of  the  key  is 
pushed  down,  contact  is  made  at  a,  the  main  circuit  is  closed, 
the  electro-magnet  of  the  relay  becomes  active,  the  lever  of  the 
relay  is  drawn  forward,  contact  is  made  at  b,  the  local  circuit  is 
closed,  the  electro-magnet  of  the  sounder  becomes  active,  and 
the  lever  of  the  sounder  is  drawn  down.  Thus,  the  levers  of  the 
relay  and  sounder  vibrate  in  unison,  but  each  is  worked  by  a 
different  battery.  The  vibration  of  the  lever  of  the  relay  is 
controlled  by  the  key,  and  controls  the  vibration  of  the  lever  of 
the  sounder  by  opening  and  closing  the  local  circuit. 

363.  The  two  Terminal  Stations  of  a  Line.  —  Figure  301 
shows  the  arrangement  of  the  instruments  and  circuits  for  two 
terminal  stations.  For  convenience,  half  of  the  main  battery  is 
placed  at  each  station.  There  is  also  a  key,  a  relay,  and  a 
sounder  at  each  station.  One  pole  of  the  main  battery,  say  the 
negative,  at  New  York  is  connected  with  the  earth  by  a  wire 
running  to  a  large  copper  plate  E  sunk  in  the  ground.  A 
wire  runs  from  the  positive  pole  of  the  battery  to  the  anvil  of 
the  key  A",  then  from  the  lever  of  the  key  to  the  electro-magnet 
of  the  relay  /?,  then  from  the  relay  to  the  line  and  along  the  line 
to  Boston,  then  to  the  electro-magnet  of  the  relay  R ',  then  to 
the  lever  of  the  key  Af ',  then  from  the  anvil  of  the  key  to  the 
negative  pole  of  this  part  of  the  main  battery,  and  from  the  posi- 
tive pole  of  the  battery  to  the  copper  plate  E'  in  the  earth.  The 
circuit  is  completed  by  the  earth,  the  electricity  passing  one 
way  over  the  line  and  back  through  the  earth.  Each  local  bat- 
tery is  connected  with  its  relay  and  sounder  as  in  the  previous 
section. 

When  the  line  is  not  in  operation,  the  main  circuit  is  closed 
at  each  key  by  pulling  the  side  lever  H  seen  in  Figure  291  up 
against  the  anvil.  This  connects  the  axis  of  the  lever  with  the 
anvil,  and  closes  the  circuit,  although  the  levers  of  the  keys  are 
up.  The  electro-magnets  of  both  relays  are  now  active,  the 
levers  of  both  relays  are  drawn  forward,  both  local  circuits  are 
closed,  the  electro-magnets  of  both  sounders  are  active,  and 
the  levers  of  both  sounders  are  drawn  down.  When  the  ope- 
rator at  one  of  the  stations  wishes  to  send  a  message,  he  pulls 


248 


ELEMENTS    OF 


a 


NATURAL    PHILOSOPHY.  249 

back  the  side  lever  of  his  key.  This  opens  the  main  circuit, 
and  causes  all  the  electro-magnets  to  become  inactive,  and  all 
the  levers  to  be  thrown  back.  On  working  his  key,  the  levers 
of  both  relays  and  of  both  sounders  are  made  to  vibrate. 
His  own  sounder  elides  as  well  as  that  at  Boston.  When  the 
operator  has  finished  his  message,  he  closes  his  key  by  pulling 
the  side  lever  against  the  anvil.  Should  both  operators  start 
at  the  same  instant  to  send  messages,  the  fact  would  be  revealed 
by  the  confusion  of  ,the  signals  given  by  each  sounder,  and  one 
operator  would  close  his  key  and  wait  for  the  other  to  finish. 
Should  the  operator  at  the  receiving  station  desire  to  interrupt 
the  one  sending  the  message  to  ask  him  to  repeat,  or  for  any 
other  purpose,  he  Las  merely  to  open  his  key  so  as  to  break  the 
circuit. 

364.  A  Way  Station.  —  One  of  the  simplest  methods  of 
introducing  the  instrument  of  a  way  station  into  the  circuit  is 
shown  in  Figure  302.  A  and  B  are  two  brass  buttons,  turning 
on  pivots  at  the  top.  Under  the  bottom  of  each  button,  as  it 
stands  in  the  diagram,  is  a  metallic  disc  D,  E.  A  wire  runs 
from  one  of  the  metallic  discs  to  the  electro-magnet  of  the  key 
K',  and  thence  to  the  anvil  of  the  key  K' '.  A  wire  runs  from 
the  other  disc  to  the  lever  of  the  key.  There  is  a  third  metallic 
disc  at  C  between  the  buttons.  When  the  buttons  are  on  the 
discs  D  and  E,  the  key  and  the  electro-magnet  of  the  relay  are 
in  the  main  circuit.  The  sounder  and  local  circuit  are  arranged 
precisely  as  in  the  terminal  stations.  When  not  in  operation, 
the  key  is  kept  closed  by  means  of  the  side  lever. 

It  will  be  seen  at  once  that  the  levers  of  the  relay  and 
sounder  will  vibrate  when  the  key  at  either  terminal  station  is 
worked,  and  also  that  the  levers  of  the  relays  and  sounders  at 
the  terminal  stations  will  vibrate  on  working  the  key  at  the  way 
station.  When  the  buttons  A  and  B  are  both  turned  upon  the 
disc  C,  the  instrument"  of  the  way  station  will  be  cut  out  of  the 
circuit,  which  will  be  completed  through  the  buttons,  these  being 
now  in  contact  with  each  other. 

When  any  key  at  any  station  is  worked,  the  sounders  of 
every  station  which  is  not  cut  out  will  click.  The  name  of  the 
station  for  which  the  message  is  designed  is  first  called,  and 
only  the  operator  at  that  station  attends  to  the  message. 


250 


ELEMENTS   OF 


•0 


« 


« 


-D 


NATURAL   PHILOSOPHY.  251 

There  are  means  at  each  way  station  to  connect  one  of  the 
wires  with  the  ground  and  the  other  wire  with  the  line  on  either 
side,  so  that  the  operator  may  use  that  side  alone,  in  case  the 
line  is  injured  in  any  way  on  the  other  side>of  his  station.  The 
chief  reason  for  dividing  the  main  battery  between  the  terminal 
stations  is  to  enable  a  way  station  to  use  the  line  on  either  side 
in  case  of  necessity. 

F.   TRANSMISSION  OF  POWER  BY  MEANS  OF  ELECTRICITY. 

365.  Electro- Motors.  —  The  current  produced  by  moving 
a  magnet  near  a  wire,  or  a  wire  near  a  magnet,  always 
opposes  the  motion  which  produces  it ;  that  is  to  say,  it  tends 
to  produce  motion  in  the  opposite  direction.  Hence,  if  a  cur- 
rent of  electricity  from  any  external  source  were  sent 
through  the  coils  of  a  magneto-electrical  machine  in  the 
direction  of  the  one  produced  in  these  coils  by  the  action 
of  the  machine,  it  would  cause  the  cylinder  to  revolve  in 
the  opposite  direction  to  that  in  which  it  must  be  turned  to 
produce  a  current.  Hence  electricity  when  sent  through 
the  coils  of  such  a  machine  becomes  a  source  of  power. 
A  machine  driven  by  electricity  is  called  an  electro-motor. 

It  is  proposed  to  employ  electricity  as  a  motive  power  for  a 
great  variety  of  purposes.  Companies  have  been  formed  to 
develop  electric  currents  at  one  or  more  centres  in  cities,  and 
send  them  through  wires  laid  in  the  streets  to  the  houses,  to  be 
used  for  a  variety  of  domestic  purposes,  such  as  driving  clocks, 
working  sewing-machines,  pumping  water,  etc. 

It  is  thought  that  electricity  will  be  found  to  be  the  medium 
by  which  power  can  be  most  efficiently  and  economically  trans- 
mitted to  a  distance.  For  instance,  if  water-power  is  abun- 
dant in  places  remote  from  the  localities  where  the  power  is 
needed,  the  energy  of  the  water  may  be  converted  into  that  of 
electricity  by  means  of  dynamo-electrical  machines,  then  the 
electricity  conducted  to  the  distant  points  through  wires,  and 
used  as  a  source  of  power  with  similar  dynamo-electrical  ma- 
chines (357). 


252 


ELEMENTS    OF 


Fig.  3°3- 


Fig.  304. 


G.   ELECTRO-THERMAL  ACTION. 

366.  Thermo- Electric  Piles.  —  When    two    metals    are 
soldered  together,  so  as  to  form  a  closed  circuit,  as  shown 

in  Figure  303,  and  one  of  the  junctions  is 
heated  more  than  the  other,  a  current  flows 
around  the  circuit.  The  direction  and  strength 
of  the  current  vary  with  the  metals  used. 
Such  a  combination  of  two  metals  is  called 
a  thermo-electric  pair.  Antimony  and  bismuth  form  the 
best  combination  among  the  metals.  In  this  combination 
the  current  flows  across  the  heated  junction  from  the 
bismuth  to  the  antimony. 

With  a  single  pair  of  metals  only  a  feeble  current  is 
obtained.  These  pairs  may  be  combined  so  as  to  form 
batteries,  or  piles.  The  pairs  are  sol- 
dered together  at  alternate  ends,  as 
shown  in  Figure  304.  Several  hundred 
pairs  are  often  combined  in  a  pile. 

The  least  difference  of  temperature  be- 
tween the  ends  of  such  a  pile  gives  rise 
to  a  current.  When  used  in  connection 
with  a  delicate  galvanometer  the  thermopile  becomes  an 
exceedingly  sensitive  differential  thermometer  (179).  No 
current  is  obtained  from  the  pile  when  the  two  faces  are 
heated  equally. 

367.  The  Development  of  Heat  by  means  of  the  Ctirrent. 
—  Whenever  a  powerful  current  of  electricity  flows  through 
a  wire  it  heats  it.     The  flner  the  wire,  and  the  lower  the  con- 
ducting power  of  the   material   of  which    it   is   composed, 
the  more  intense  the  heat  developed.     The  more  powerful  the 
current  employed,  the  more  intense  the  heat  with  the  same 
conductor.     Fine  wires  of  the  most   refractory  metals  are 
heated  white-hot,  and  even  fused,  on  the  passage  of  power- 
ful currents. 


NATURAL    PHILOSOPHY. 


253 


368.  Electric  Illumination  by  Incandescence.  —  There  has 
been  for  a  long  time  an  effort  to  make  electricity  available 
as  a  source  of  light,  and  at  last  the  many  practical  diffi- 
culties that  have  been  met  with  seem  to  have  been  nearly, 
if  not  quite,  surmounted.     Illumination  by  means  of  a  poor 
conductor  heated  to  a  white  heat  on  the  passage  of  the  cur- 
rent,  is  called  illumination   by  incandescence.      The  great 
difficulty  encountered  in  illumination  by  incandescence  is 
that  the  conductor  which  is  heated   to    incandescence  is 
also  apt  to  be  destroyed  by  the  current.     Even  so  refrac- 
tory a  substance  as  platinum  is  very  likely  to  fuse  when 
heated  to  incandescence.     If  the  current  is  sent  through  a 
very  thin  rod  of   carbon,  the  carbon  becomes  heated  to 
incandescence ;  but  at  the  high  temperature  the  carbon  is 
liable  to  be  destroyed  by  combining  with  the  oxygen  of 
the  air.     Even  when  the  carbon  is  placed  in  an  exhausted 
receiver,  or  in  one  which  has  been  first  exhausted  of  air 
and  then  filled  with  some  gas  which  is 

a  non-supporter  of  combustion,  the  rod 
or  filament  is  liable  to  disintegration. 

369.  The  Edison  Lamp.  —  The  Edison 
lamp  for  incandescence  is  shown,  in  section, 
in  Figure  305.     The  upper  portion  of  the 
lamp  is  a  glass  globe,  from  which  the  air 
has  "been  exhausted,  and  which  is  hermeti- 
cally sealed.     In  the  centre  of  this  globe 
is  the    carbon    filament,  bent  in    the  form 
of  a  ring.     The  ends  of  this  filament  are 
held  in  little   clamps,  connected   with   the 
platinum   wires    which    pass    through    the 
glass  of  the  smaller  globe  under  the  ring, 
and  thence  out  through  the  bottom  of  the 
lamp,  where  they  are  connected  with  the 
wires  of  the  circuit. 

The  permanent  success  of  this  and  simi- 
lar lamps  for  illumination   depends   solely  upon  whether   the 


Fig.  305. 


254 


ELEMENTS    OF 


carbon  filament  is  found,  in  practice,  to  be  sufficiently  durable. 
The  Edison  filament  is  constructed  of  bamboo-wood.  The  re- 
sistance of  the  loop  is  from  100  to  300  ohms  (330),  and  the 
amount  of  light  that  can  be  safely  obtained  from  it  varies  from 
2  to  10  candles. 

These  lamps  will  be  arranged  in  the  houses  just  as  gas- 
jets  are  now,  and  electricity  will  be  conducted  to  them  by  wires 
in  the  streets,  just  as  gas  is  conducted  to  the  gas-jets  by  pipes 
in  the  streets. 

Edison's  plan  is  to  measure  the  electricity  used  in  each  house 
by  a  kind  of  voltameter  (345),  in  which  sulphate  of  copper  is 
decomposed  instead  of  sulphuric  acid.  The  copper  is  deposited 
on  one  of  the  electrodes  and  so  increases  its  weight.  The 
increase  in  weight  of  the  plate  will  show  the  amount  of  elec- 
tricity which  has  passed  through  the  instrument. 

Illumination  by  incandescence  is  especially  adapted  for  light- 
ing rooms  of  the  ordinary  size. 

Fig.  306. 


370.  The  Voltaic  Arc.  —  If  two  pencils  of  coke  carbon 
are  brought  in  contact  in  a  circuit  through  which  a  power- 
ful current  of  electricity  is  passing,  and  are  then  separated 
a  little,  intense  light  and  heat  will  be  developed  at  the  point 
of  separation  (Figure  306).  The  ends  of  the  pencils  will 
be  heated  white-hot,  and  they  will  be  connected  by  a 
luminous  bridge.  This  bridge  is  called  the  voltaic  arc. 


NATURAL   PHILOSOPHY. 


255 


The  light  and  heat  of  the  voltaic  arc  are  the  most  intense 
that  can  be  obtained  by  artificial  means. 

If  the  carbons  are  separated  far  enough  to  stop  the 
current,  it  will  not  start  again  till  they  have  been  again 
brought  in  contact.  After  the  current  has  been  started,  it 
will  continue  to  flow  after  the  carbons  are  separated,  pro- 
vided they  are  not  separated  too  far.  As  the  carbons 

Fig.  307. 


begin  to  separate,  the  current  which  is  passing  detaches 
little  particles  from  each  of  them  and  transfers  these  to 
the  other  carbon,  and  so  bridges  over  the  space  between 
the  points  with  carbon  dust.  The  air  thus  filled  with 
particles  of  carbon  offers  less  resistance  to  the  current 
than  the -air  free  from  carbon  dust  which  separates  the 
points  before  they  are  brought  into  contact  Heated  air 


256  ELEMENTS   OF 

moreover,  offers  less  resistance  than  cold  air.  The  intense 
heat  of  the  voltaic  arc  is  due  to  the  resistance  which  the 
current  encounters  in  the  space  between  the  carbon  points. 

The  end  of  the  positive  carbon  becomes  concave,  and 
that  of  the  negative  carbon  pointed,  as  shown  in  Figure 
307.  Both  carbons  are  consumed,  but  the  positive  more 
rapidly  than  the  negative. 

371.  Illumination  by  the  Voltaic  Arc.  —  In  order  to  ob- 
tain illumination  by  the  voltaic  arc,  a  lamp  is  needed  to 
keep  the  carbons  all  the  time  at  the  right  distance  apart, 
and  to  bring  them  together,  in  case  the  current  should 
stop,  and  then  to  separate  them  again  when  it  has  started. 

In  the  best  lamps  for  this  purpose,  the  points  are  moved  by 
means  of  clock-work,  which  is  so  constructed  that  it  can  be 
made  to  move  the  points  either  together  or  apart.  The  clock- 
work is  controlled  by  an  electro-magnet  by  means  of  a  lever. 
The  current  passes  through  the  coil  of  this  electro-magnet  on 
its  way  to  the  carbons.  When  the  carbons  become  too  far 
apart,  the  current  is  weakened,  the  lever  is  released,  and  the 
clock-work  is  made  to  turn  so  as  to  move  the  carbons  together. 
When  the  carbons  come  too  near  together,  the  current  becomes 
strong  enough  to  draw  the  lever  down,  and  this  causes  the 
clock-work  to  turn  so  as  to  separate  the  points.  When  the 
points  are  at  just  the  right  distance  apart,  the  lever  is  held  in 
such  a  position  as  to  stop  the  clock-work  entirely. 

Illumination  by  the  voltaic  arc  is  too  intense  for  rooms  of  the 
ordinary  size,  but  is  especially  adapted  for  out-door  illumination, 
and  for  large  halls  and  workshops. 


NATURAL   PHILOSOPHY.  257 


VII. 

METEOROLOGY. 

I. 
CONSTITUTION    OF   THE   ATMOSPHERE. 

372.  The   Term   Meteorology.  —  The    term    meteor  was 
formerly  applied   to   any  natural    phenomenon  occurring 
within   the    limits   of   the   atmosphere  ;   hence   the   term 
meteorology  as  applied  to  that  branch  of  Natural  Philosophy 
which  treats  of  the  atmosphere. 

373.  The  Composition  of  the  Atmosphere.  —  The  atmos- 
phere is  composed  chiefly  of  oxygen  and  nitrogen  in  a  state 
of  mechanical  mixture,  and  not  of  chemical  combination. 
In  every  100  volumes  of  air  there  are  nearly  79.1  volumes 
of  nitrogen  and  20.9  volumes  of  oxygen.     Owing  to  the 
tendency  of    these    two   gases  to  diffuse  into  each  other, 
and  to  the  currents  which  exist  in  the  atmosphere,  these 
proportions  are  sensibly  the  same  in  all  parts  of  the  globe 
and  at  all  accessible  elevations  above  its  surface. 

In  addition  to  the  oxygen  and  nitrogen,  the  atmosphere 
contains  also  a  little  carbonic  acid  and  watery  vapor.  The 
amount  of  carbonic  acid  varies,  in  the  open  country,  from 
4  to  6  parts  in  a  thousand.  The  amount  of  moisture  is 
very  variable,  ranging  from  4  parts  in  one  hundred  to  i 
part  in  a  thousand. 

374.  The  Height  of  the  Atmosphere.  —  The  atmosphere 
is  held  to  the  earth  by  gravity,  and  it  must  terminate  at 
that  height  at  which  the  attraction  of  the  earth  is  balanced 


258 


ELEMENTS   OF 


by  the  repulsion  of  the  particles  of  the  air.  At  the  height 
of  50  miles  the  atmosphere  is  wellnigh  inappreciable  in 
its  effect  upon  twilight.  The  phenomena  of  lunar  eclipses 
indicate  an  appreciable  atmosphere  to  the  height  of  66 
miles  ;  while  the  phenomena  of  shooting  stars  and  of  the 
auroral  light  show  that  such  an  atmosphere  exists  at  the 
height  of  200  or  300  miles,  and  probably  of  more  than 
500  miles,  above  the  earth's  surface. 

375.  The  Weight  of  the  Atmosphere.  —  The  weight  or 
downward  pressure  of  the  air  at  any  point  is  ascertained 
by  the  use  of  the  barometer  (126).  It  is  different  in 
different  parts  of  the  earth,  and  is  in  a  state  of  constant 
fluctuation  at  the  same  place.  If  we  observe  the  height 
of  the  barometer  every  hour  of  the  day,  and  then  divide 
the  sum  of  the  observed  heights  by  24,  we  obtain  the 
mean  height  for  the  day.  By  dividing  the  sum  of  the  daily 
means  for  a  month  by  the  number  of  days  in  the  month, 
we  obtain  the  mean  height  for  the  month.  By  dividing  the 
sum  of  the  monthly  means  for  a  year  by  12,  we  obtain  the 
mean  height  for  the  year.  If  we  divide  the  sum  of  the 
annual  means  for  a  series  of  years  by  the  number  of  years 
in  the  period,  we  obtain  the  mean  height  for  the  place. 
This  at  Boston  is  29.988  inches. 

Fig.  308. 


BOJ 

BO.O 
39.8 
30.6 
89.4 
29.2 


70'  60"  60*  40^   30°   20»   10"    0"    10°  20°  SO? 


W   ?0>   BO' 


376.  The  Mean  Height  of  the  Barometer  at  Different  Lati- 
tudes. —  The  curve  in  Figure  308  shows  the  mean  height  of  the 
barometer  at  different  latitudes  from  75°  north  to  80°  south. 
The  numbers  at  the  bottom  show  the  latitude,  and  those  at  the 
side  the  height  of  the  barometer  in  inches.  The  height  at 
which  the  curve  crosses  the  vertical  lines  of  the  diagram  shows 


NATURAL   PHILOSOPHY. 


259 


the  mean  height  of  the  barometer  at  that  latitude.  The  height 
is  found  by  following  the  horizontal  lines  to  the  left ;  and  the 
l.ititude,  by  following  the  vertical  lines  to  the  bottom.  It  will 
be  seen  from  the  diagram,  that  the  mean  height  of  the  barome- 
ter is  greatest  at  32°  north  and  25°  south  of  the  equator,  and 
lowest  at  64°  north  and  about  70°  south  of  the  equator ;  also 
that  the  mean  height  of  the  barometer  is  generally  greater  north 
of  the  equator  than  south  of  it.  There  is  a  belt  of  low  pressure 
at  the  equatdr. 

377.  The  Mean  Height  of  the  Barometer  for  Different 
Months.  —  The  mean  height  of  the  barometer  varies  somewhat 
from  month  to  month  during  the  year,  being  generally  higher  in 
winter  than  in  summer.  In  many  places  the  mean  height  in 
winter  exceeds  that  of  summer  by  half  an  inch,  while  in  other 
places  the  inequality  almost  entirely  disappears.  At  Pekin, 
China,  the  mean  height  of  the  barometer  for  January  exceeds 


Fig.  309- 


X 


JFMAMJJASONDJ 


that  for  July  by  three  quarters  of  an 
inch.  At  Boston  the  mean  pressure 
does  not  differ  more  than  one  tenth 
of  an  inch  for  any  two  months  of  the 
year.  The  same  is  true  of  London 
and  Paris.  The  four  curves  B,  L,  H, 
and  P  (Figure  309)  show  the  monthly 
fluctuations  of  the  mean  pressure  at 
Boston,  London,  Havana,  and  Pekin. 
The  spaces  and  letters  at  the  bottom 
represent  the  months,  and  the  verti- 
cal lines  the  height. 

378.  Hourly  Fluctuation  of  the  Barometer. —  When  the  in- 
dications of  the  barometer  for  each  hour  of  the  day  for  a  long 
period  are  averaged,  it  will  be  found  that  these  averages  are  not 
equal.     The  height  of  the  barometer  is  greatest  about  10  A.  M. 
and  least  at  about  4  P.  M.     There  are  also  smaller  fluctuations 
at  night,  the  barometer  attaining  a  second  maximum  at  about 
10  P.  M.  and  a  second  minimum  at  about  4  A.  M.     This  diurnal 
oscillation   is  greatest  at  the  equator,   and  decreases  as   we 
approach  either  pole. 

379.  Fluctuation  depending  on  the  Position  of  the  Moon.  — 
There  is  a  small  fluctuation  of  the  barometer  depending  on  the 


260  .          ELEMENTS    OF 

position  of  the  moon,  but  this  variation  is  exceedingly  minute 
and  can  be  detected  only  by  taking  the  mean  of  the  most  accu- 
rate observations  continued  for  a  long  time.  These  fluctuations 
indicate  a  feeble  tide  in  the  atmosphere  similar  to  those  of  the 
ocean. 

380.  Irregular  Fluctuations.  —  The    irregular    fluctuations 
of  the  barometer  are  far  greater  than  the  periodic  ones.     The 
difference  between  the  greatest  and  least  heights  of  the  barom- 
eter for  a  single  month  is  called  the  monthly  oscillation,  and  by 
combining  observations  extending  over  a  series  of  years  we 
obtain  the  mean  monthly  oscillation.     This  is  least  at  the  equa- 
tor, and  increases  as  we  proceed  towards  the  poles. 

•  At  the  equator  it  is  about  ^  of  an  inch  ;  in  latitude  30°  it  is 
^  of  an  inch  ;  in  latitude  45°,  over  the  Atlantic  Ocean,  it  is 
I  inch;  in  latitude  65°  it  is  \\  inches.  The  extreme  fluctua- 
tions are  much  greater  than  the  mean  monthly  oscillations. 
The  greatest  and  least  observed  heights  of  the  barometer  at 
Boston  are  31.125  inches  and  28.47  inches,  the  difference  being 
2.655  inches.  The  greatest  observed  difference  at  London  is 
3  inches;  and  at  St.  Petersburg,  3.5  inches. 

II. 
TEMPERATURE  OF  THE  ATMOSPHERE. 

381.  How  the  Atmosphere  becomes  Heated.  —  The  atmos- 
phere becomes  heated  partly  by  absorbing  the  direct  rays  of 
the  sun,  partly  by  contact  with  the  warmer  earth,  and  partly 
by  absorbing  the  obscure  heat  radiated  from  the  earth. 

A  -portion  of  the  heat  emitted  by  the  sun  is  absorbed  by  our 
atmosphere  before  it  can  reach  the  earth's  surface.  It  is  esti- 
mated that  on  a  clear  day  our  atmosphere  absorbs  about  one 
fourth  of  the  rays  which  traverse  it  vertically.  The  heat  thus 
absorbed  raises  the  temperature  of  the  atmosphere.  It  is 
mainly  the  obscure  rays  (220)  that  are  absorbed  by  the  atmos- 
phere, and  this  absorption  is  done  chiefly  by  the  watery  vapor 
in  the  atmosphere.  The  rays  of  the  sun  which  reach  the  earth's 
surface  are  absorbed  by  it.  The  surface  thus  becomes  heated, 
and  communicates  heat  to  the  air  which  rests  upon  it.  This 


NATURAL    PHILOSOPHY. 


26l 


heated  air,  becoming  lighter  through  expansion,  rises  and  gives 
place  to  colder  air  from  above,  which  in  turn  becomes  heated 
by  contact  with  the  earth. 

As  the  surface  of  the  earth  becomes  warmed  by  the  direct 
rays  of  the  sun,  it  radiates  obscure"  heat  back  into  the  atmos- 
phere. These  rays  are  partially  absorbed  by  the  atmosphere, 
especially  in  the  lower  layers,  where  watery  vapor  is  most 
abundant  (224,  225). 

382.  Hourly  Variations  of  Temperature. — The  temper- 
ature of  a  place  varies  from  hour  to  hour  according  to  the 
elevation  of  the  sun  above  the  horizon.  The  average  of 
observations  taken  for  a  long  period  shows  that  the  mean 
hourly  variations  of  temperature  are  extremely  regular. 
The  curve  in  Figure  310  shows  the  mean  hourly  variations 

Fig.  310. 


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oo- 

5i; 

^^ 

—  -~ 

-" 

/ 

• 

(>_ 

/ 

\ 

4S'- 
4G= 

/ 

•• 

.. 

X 

s. 

/ 

v  — 

42« 

iu- 

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12    2      4     G      8     10     n     2      4      6      8    10   12 

of  temperature  at  New  Haven.  There  is  a  maximum  and 
minimum  of  temperature  each  day,  the  minimum  occurring 
about  an  hour  before  sunrise,  and  the  maximum  about  two 
hours  after  noon. 

The  highest  temperature  of  the  day,  other  things  being  equal, 
occurs  when  the  amount  of  heat  lost  each  instant  by  radiation 
is  just  equal  to  that  received  from  the  sun.  Before  midday  the 
earth  receives  more  heat  from  the  sun  than  it  loses  by  radia- 
tion, and  the  temperature  rises.  After  noon  the  earth  receives, 
each  instant,  less  heat  from  the  sun  than  it  did  at  noon ;  but  for 
some  time  it  still  receives  heat  faster  than  it  parts  with  it. 
Hence  the.  maximum  of  temperature  occurs  some  time  after 
noon.  During  the  night  we  receive  no  direct  heat  from  the  sun, 


262 


ELEMENTS   OF 


and  the  earth  cools  by  radiation.  About  an  hour  before  sunrise 
the  heat  received  from  the  returning  sun  becomes  equal  to  that 
lost  by  radiation,  and  the  temperature  ceases  to  fall. 

383.  Mean  Temperature  of  a  Day.  —  The  mean  temper- 
ature of  a  day  is  the  average  temperature  of  the  24  hours. 
This  is  found  by  taking  the  average  of  three  observations, 
one  at  6  A.  M.,  one  at  2  P.  M.,  and  one  at  9  P.  M. 

384.  Monthly  Variations  of  Temperature.  —  The  curves 
of  Figure  311  show  the  mean  temperature  and  also  the 

Fig.  3ir.  mean    maximum   and   minimum 

temperatures  for  each  month  of 
the  year  at  New  Haven,  accord- 
ing to  observations  extending 
through  86  years.  The  months 
are  given  on  the  horizontal  line 
at  the  bottom,  and  the  degrees 
of  temperature  on  the  vertical 

^ne  at  ^e  k^  ^ie  warmest 
months  of  the  year  for  this  place 

are  July  and  August,  the  maximum  occurring  about  the 
24th  of  July.  The  coldest  month  is  January,  the  mini- 
mum occurring  about  the  2ist  of  this  month.  The  differ- 
ence between  the  maximum  and  minimum  temperature  is 
greater  for  the  cold  than  for  the  warm  months. 

The  chief  reasons  why  it  is  colder  during  the  winter  months 
than  during  the  summer  months  are  that  the  sun  is  farther 
from  the  zenith  and  is  a  shorter  time  above  the  horizon.  The 
earth  is  receiving  the  most  heat  from  the  sun  at  the  time  of  the 
summer  solstice,  but  the  temperature  continues  to  rise  as  long 
as  the  earth  receives  more  heat  from  the  sun  during  the  day 
than  it  loses  by  radiation  during  the  night.  During  the  autumn 
the  loss  at  night  is  much  greater  than  the  gain  by  day,  and  the 
temperature  rapidly  falls.  The  temperature  continues  to  fall  till 
the  gain  by  day  is  again  equal  to  the  loss  by  night.  This  does 
not  occur  till  some  time  after  the  winter  solstice. 

385.  Irregular  Fluctuations  of  Temperature.  —  Besides 


NATURAL   PHILOSOPHY.  263 

the  periodic  variations  of  temperature,  there  are  irregular 
fluctuations  of  temperature  which  are  liable  to  occur  any 
hour  of  the  day  and  any  day  of  the  year. 

386.  Variations  of  Temperature  with  the  Latitude.  —  As 
we  proceed  from  the  equator  to  the  poles,  the  temperature 
generally  falls,  but  not  at  a  uniform  rate,  and  the  rate  of 
fall  is  different  on  different  meridians.     Hence  the  lines 
of  equal  temperature  on  the  surface  of  the  earth  do  not 
coincide  with  the  parallels  of  latitude.     Lines  which  con- 
nect places  of  equal  mean  temperature  are  called  isothermal 
lines.     The  isothermal   lines   for  every  ten   degrees   are 
shown  on  the    accompanying   map   (Figure  312).     They 
are   much  more  irregular   on   and  around  the  continents 
than  in  the  oceans. 

387.  The  Temperature  of  the  two  Sides  of  the  Atlantic.  — 
It  will  be  seen  from  the  map  in  Figure  312  that  the  mean 
temperature  of  the  eastern  side  of  the  Northern  Atlantic 
Ocean  is  considerably  higher  than  that  of  the  western  side  at 
the  same  latitude.     The  temperature  of  Dublin  is  as  high 
as   that  of  New  York,  though  the  former  is    13°  farther 
north,  while  near  Lake  Superior,  in  latitude  50°,  we  find 
the  same  mean  temperature  as  at  the  North  Cape,  in  lati- 
tude 72°. 

The  high  temperature  of  the  European  coast  is  due  to  the 
high  temperature  of  the  Northern  Atlantic  and  the  prevalent 
westerly  winds.  The  Gulf  Stream  conveys  the  warm  water  of 
the  equatorial  region  into  the  North  Atlantic.  The  temperature 
of  the  North  Atlantic  is  thus  raised  considerably  above  what  is 
due  to  its  latitude,  and  the  prevalent  westerly  winds  of  the 
middle  latitudes  carry  this  heat  to  the  eastern  side  of  the  Atlan- 
tic and  away  from  its  western  side. 

388.  The  Temperature  of  the  two  Sides  of  the  Pacific.  — 
Owing  to  the  currents  of  the  Pacific  Ocean,  there  is  a  cor- 
responding difference  of  temperature  between  its  eastern 
and  western  coast,  the  temperature  of  the  east  coast  being 


264 


ELEMENTS    OF 


NATURAL   PHILOSOPHY.  265 

higher  than  that  of  the  west.  This  causes  a  marked  dif- 
ference of  temperature  between  the  eastern  and  western 
coasts  of  North  America  at  places  on  the  same  parallel. 
The  same  isothermal  line  will  be  found  10  or  15  degrees 
farther  north  on  the  Pacific  coast  of  North  America  than 
"on  the  Atlantic  coast. 

389.  The    Temperature   of  the  Northern   and  Southern 
Hemispheres.  —  The    mean    temperature    of    the   northern 
hemisphere  is  nearly  three  degrees  higher  than  that  of  the 
southern  hemisphere. 

The  unequal  temperature  of  the  two  hemispheres  is  probably 
due  to  the  unequal  distribution  of  land  and  water.  The  north- 
ern hemisphere  contains  more  land  and  less  water  than  the 
southern.  In  the  southern  hemisphere  the  sun's  rays  fall  chiefly 
upon  water,  and  a  large  amount  of  heat  is  consumed  in  evapo- 
ration. In  the  condensation  of  vapor  the  heat  is  again  liberated. 
Observations  show  that  there  is  more  condensation  in  the 
northern  hemisphere  than  in  the  southern.  Thus  the  southern 
hemisphere  is  cooled  more  by  evaporation  and  warmed  less  by 
condensation  than  the  northern  hemisphere. 

390.  Mean  and  Extreme  Temperatures  of  a  Place.  —  Two 
places  having  the  same  mean  temperature  may  differ  greatly  in 
their  extreme  temperatures.     New  York  and  Liverpool  have  the 
same  mean  temperature,  but  the  difference  between  the  mean 
temperature  of  the  three  summer  months  and  that  of  the  three 
winter  months  is  twice  as  great  in  New  York  as  in  Liverpool. 

In  some  localities  the  mean  temperature  of  the  hottest  month 
of  the  year  is  less  than  5°  above  that  of  the  coldest,  while  in 
other  localities  it  is  70°  or  80°  above. 

391.  Marine  and  Continental  Climates.  —  The  tempera- 
ture of  water  changes  less  than  that  of  land. 

The  specific  heat  (197)  of  water  being  much  higher  than 
that  of  land,  a  \nuch  greater  amount  of  heat  is  consumed  in 
raising  the  temperature  of  an  equal  mass  of  water  the  same 
number  of  degrees,  and  a  much  greater  amount  of  heat  is  liber- 
ated in  the  cooling  of  an  equal  mass  of  water.  Hence  when  land 
and  water  are  receiving  or  losing  heat  at  the  same  rate,  the 


266  ELEMENTS   OF 

temperature  of  the  former  will  rise  higher  or  fall  lower  than 
that  of  the  latter  in  the  same  time.  The  high  latent  heat  of 
watery  vapor  (202)  tends  to  keep  the  temperature  of  water 
uniform,  a  large  amount  of  heat  being  rendered  latent  by  evapo- 
ration when  the  temperature  is  rising,  and  an  equally  large 
amount  being  liberated  by  condensation  when  the  temperature 
is  falling.  Again,  the  sun's  rays  penetrate  water  to  a  greater 
depth  than  land,  and  at  the  same  time  the  currents  in  the  ocean 
tend  to  equalize  the  temperature  of  the  water  at  different 
depths.  Hence,  while  land  becomes  heated  only  at  the  surface, 
water  becomes  heated  to  a  considerable  depth  below  the  sur- 
face. The  greater  depth  of  water  heated  and  cooled  as  the 
temperature  rises  and  falls  would  cause  the  temperature  to 
change  less  at  the  surface  of  water  than  of  land. 

When  the  temperature  of  a  place  is  controlled  mainly  by  the 
ocean,  the  temperature  is  equable,  and  the  climate  is  called 
marine;  when,  on  the  contrary,  it  is  controlled  mainly  by  the 
continent,  the  temperature  is  extreme,  and  the  climate  is  called 
continental.  On  the  eastern  coast  of  the  United  States,  where 
the  prevalent  winds  are  from  the  land,  there  is  a  great  annual 
range  of  temperature  and  a  continental  climate  ;  while  in  the 
western  part  of  Europe,  where  the  prevalent  winds  are  from 
the  ocean,  the  temperature  is  more  uniform  and  the  climate 
marine. 

392.  Change  of  Temperature  with  the  Elevation.  —  As 
we  ascend  in  the  atmosphere  from  the  earth,  the  tempera- 
ture falls.  The  rate  of  decrease  varies  with  the  latitude 
of  the  place,  with  the  time  of  the  year,  and  with  the  hour 
of  the  day.  It  is  more  rapid  in  warm  countries  than  in 
cold,  and  in  the  hot  months  than  in  the  cold.  It  is 
most  rapid  about  5  P.  M.,  and  least  rapid  about  sunrise. 
The  change  is  also  most  rapid  near  the  earth,  and  decreases 
as  we  ascend. 

There  are  two  main  reasons  why  the  temperature  of  the 
atmosphere  falls  as  we  ascend  :  (i)  The  air  of  the  earth's  sur- 
face becomes  heated  and  expanded,  and  tends  to  rise  because 
of  its  diminished  specific  gravity.  As  the  air  ascends  it  meets 


NATURAL   PHILOSOPHY.  267 

with  less  pressure  and  therefore  expands  ;  this  expansion  con- 
sumes heat  (204),  and  causes  the  temperature  to  fall.  (2)  The 
moisture  in  the  air  becomes  less  and  less  as  we  ascend,  and 
hence  there  is  less  absorption  of  the  solar  rays,  and  it  is  only 
the  rays  which  are  absorbed  that  tend  to  raise  the  temperature ; 
there  also  is  less  hindrance  to  the  escape  into  space  of  the  heat 
radiated  from  the  atmosphere. 

393.  The  Line  of  Perpetual  Snow.  —  Since  the  tempera- 
ture of  the  atmosphere  falls  as  we  ascend,  the  tops  of 
high  mountains,  even  "within  the  tropics,  are  covered  with 
perpetual  snow.      The  snow-line  depends  more  upon  the 
temperature  of  the  hottest  month  than  upon  the  mean  tem- 
perature of  the  year.     It  is  not  therefore  the  line  whose 
mean  temperature  is  32°.     It  depends  also  to  a  consider- 
able extent  upon  the  annual  snow-fall. 

Under  the  equator  the  height  of  the  snow-line  varies  from 
15,000  to  16,000  feet,  where  the  mean  annual  temperature  is 
35°.  On  the  Alps  the  average  height  of  the  snow-line  is  8800 
feet,  where  the  mean  annual  temperature  is  25°  ;  while  on  the 
coast  of  Norway  its  height  is  only  2400  feet,  where  the  mean 
annual  temperature  is  21°. 

394.  The  Atmosphere   a   Regulator   of    Temperature. — 
During  the  day  the  atmosphere  absorbs  a  portion  of  the 
sun's  rays,  so  that  they  are  less  excessive  on  reaching  the 
earth.     A  considerable  portion  of  the  heat  thus  absorbed 
during  the  day  is  rendered  latent  by  expansion.     At  night 
the  air  intercepts  a  part  of  the  rays  emitted  by  the  earth, 
and  so  keeps  the  heat  from  escaping  into  space.     At  the 
same  time,  as  the  air  is  cooled,  it  contracts,  and  so  liberates 
the  heat  that  was  rendered  latent  by  expansion  during  the 
day.     Were  it  not  for  the  atmosphere  the  days  would  be 
very  much  hotter  and  the  nights  very  much  colder  than 
they  are  now.     It  is  chiefly  by  means  of  the  watery  vapor 
present  in  the  atmosphere  that  it  acts  thus  as  a  regulator 
of  temperature  (381). 


268 


ELEMENTS   OP 


III. 


HUMIDITY   OF   THE    ATMOSPHERE. 

395.  The  Hygrometer.  —  An  instrument  capable  of  meas- 
uring the  moisture  of  the  air  is  called  a  hygrometer.  A 
hygroscope  is  an  instrument  which  merely  shows  that  there 
are  changes  of  moisture,  without  being  capable  of  measuring 
xthe  amount  of  moisture  present.  t 

Mason's  hygrometer  (Figure  313)  consists  of  two  thermome- 
ters. The  bulb  of  one  of  these 
is  kept  moist  by  being  covered 
with  muslin  or  silk,  the  fibres  of 
which  dip  into  a  reservoir  of 
water.  The  water  is  drawn  up 
to  the  bulb  by  capillary  action, 
and  the  evaporation  from  its 
surface  lowers  its  temperature. 
Hence  the  wet-bulb  thermometer 
will  always  show  the  lower  tem- 
perature. The  greater  the  dif- 


Fig.  313- 


ference  of  reading  between  the 
thermometers,  the  faster  the 
evaporation  from  the  wet  bulb 
and  the  drier  the  air. 

396.  The  Humidity  of  the 
^2>.  —  The  amount  of  moist- 
ure which  a  cubic  foot  of  air 
can  hold  increases  with  the 
temperature.  When  the  air 
contains  all  the  moisture  it  can 
hold  at  that  temperature,  it  is  said  to  be  saturated  with 
moisture.  By  the  humidity  of  the  air  we  do  not  mean  the 
absolute  amount  of  moisture  in  it,  but  its  degree  of  satura- 
tion. If  the  air  is  half  saturated,  its  humidity  is  50:  if 
three-quarters  saturated,  75  ;  etc. 


NATURAL   PHILOSOPHY.  269 

397.  The  Dew- Point.  —  The  dew-point  is  the  temperature 
at  which  the  air  would  become  saturated  with  the  moisture 
in  it,  and  its  moisture  begin  to  be  deposited  as  dew.     It  is 
not  a  fixed   temperature,   like   those  of  the  freezing  and 
boiling  points,  but  varies  with  the  temperature  and  humidity 
of  the  air.     The  greater  the  humidity  of  the  air,  the  less 
the   temperature   would   have   to  fall  to  reach  the   dew- 
point. 

398.  Diurnal  Variation  in  the  Vapor  in  the  Atmosphere. 

—  The  amount  of  vapor  in  the  atmosphere  is  subject  to 
great  fluctuations,  some  of  which  are  irregular  and  others 
periodic.      As  a  rule,  the  amount  is  least  about  an  hour 
before   sunrise,   and   greatest  just  before  sunset,   the    mean 
diurnal   variation   amounting  to  about  }&  of  the  average 
amount  of  vapor  present. 

The  curve  in   Figure   314   shows   the    diurnal   variation  at 
Philadelphia,  the  figures  at  the  Fig  3,4 

left  indicating  the  pressure  of 
the  vapor  in  inches  of  mercury  & 
at  the  hours  given  at  the  bot-  -30 
torn.  This  variation  is  due  to 
the  diurnal  change  in  tempera- 
ture. As  the  temperature  rises  during  the  day,  more  water  is 
evaporated  from  the  ocean  and  the  moist  earth,  and  the  amount 
of  vapor  in  the  air  increases.  During  the  night  a  portion  of  the 
vapor  is  condensed  in  the  form  of  dew  and  hoar-frost,  and  the 
amount  present  in  the  air  decreases. 

399.  Annual    Variation  in   the   Amount  of  Vapor  in   the 
Atmosphere.  —  In  the  northern  hemisphere   the  mean  amount 
of  vapor  in  the  atmosphere  is  greatest  in  July,  when  the  mean 
temperature  is  highest,  and  least  in  January,  when  the  mean 
temperature  is  lowest.     This  is  due  to  the  more  rapid  evapora- 
tion in  summer  than  in  winter. 

400.  Variation  in  the  Amount  of  Vapor  with  the  Elevation. 

—  The  humidity  of  the  atmosphere  as  a  rule  decreases  as  we 
rise  above  the  earth,  though  there  is  a  slight  increase  of  humid- 
ity for  the  first  3000  feet.     At  the  highest  elevations  at  which 


810D.2      4      6 


270 


ELEMENTS    OF 


observations  have  been  taken  the  air  has   never  been  found 
entirely  free  from  moisture. 

401.  Diurnal  Variation  of  the  Pressure  of  the  Gaseous 
Atmosphere. — The  earth  is  really  enveloped  in  two  atmos- 
pheres, one  of  vapor  and  one  of  permanent  gases.  These  two 
atmospheres  are  mixed  together,  and  by  their  combined  pres- 
sure cause  the  rise  of  the  barometer.  Other  things  being 
equal,  the  greater  the  amount  of  vapor  present  in  the  atmos- 
phere the  higher  the  barometer,  and  vice  versa.  Fluctuations 
in  the  height  of  the  barometer  are  caused  by  changes  in  the 
temperature  of  the  air  and  the  amount  of  vapor  present  in 
the  atmosphere.  A  diminution  of  vapor  and  an  increase  in 
temperature  both  tend  to  cause  the  barometer  to  fall. 

If  we  subtract  the  pressure  of  the  vapor  in  the  atmosphere 
from  that  of  the  whole  atmosphere,  the  remainder  will  be  the 

pressure  of  the  gaseous  at- 
mosphere. At  Philadelphia 
this  pressure  is  greatest  about 
an  hour  after  sunrise  and  least 
about  4  P.  M.,  as  is  shown  by 


Fig.  315- 


33.«2 
.60 


•   1  IDT    the  curve  of  Figure  31 5. 

402.    Annual   Variation   of 

the  Pressure  of  the  Gaseous  Atmosphere.  —  In  the  northern 
hemisphere  the  pressure  of  the  gaseous  atmosphere  '^greatest 
in  January,  when  the  temperature  is  lowest,  and  least  in  July, 
when  the  temperature  is  highest.  The  difference  between  the 
summer  and  winter  pressures  of  the  gaseous  atmosphere  is  very 
unequal  in  different  countries.,  In  the  eastern  part  of  the 
United  States  this  difference  amounts  to  about  half  an  inch, 
while  in  Central  Asia  it  amounts  to  above  an  inch,  and  at  the 
equator  is  scarcely  appreciable. 


IV. 


MOVEMENTS    OF   THE  ATMOSPHERE. 

403.     Winds.- — Wind    is  air  in  motion.     Although  the 
winds  are   proverbially  variable  and  fickle,  they  are  gov- 


NATURAL    PHILOSOPHY. 


271 


erned  by  laws  as  fixed  and  definite  as  those  which  regulate 
the  temperature  and  pressure  of  the  atmosphere. 

The  force  of  a  wind  is  estimated  either  by  its  velocity  in 
miles  per  hour  or  by  its  pressure  in  pounds  per  square  foot. 
The  character,  velocity,  and  pressure  of  various  winds 
are  given  in  the  following  table,  taken  from  Loomis  :  — 


Character. 

Velocity 
in  Miles 
per 
Hour. 

Force  in 
Pounds 
per  Square 
Foot. 

2 

o  0° 

Gently  pleasant     

008 

Pleasant  brisk       .... 

T->I/ 

Very  brisk   - 

*-/2 

**7i 

*i  no 

<O 

j.UU 

6 

Very  high  wind     .... 

35 

A  e 

IO 

Strong  gale  

4i 
60 

18 

Violent  gale 

7O 

fA 

Hurricane     

80 

-1\ 

Most  violent  hurricane  

ICO 

40 

From  a  long  series  of  observations  at  Philadelphia,  it  appears 
that  the  mean  velocity  of  the  wind  is  1 1  miles  an  hour.  The 
mean  velocity  varies  somewhat  during  the  day  and  during  the 
year.  It  is  least  about  sunrise  and  greatest  about  2  P.M.  It  is 

Fig.  316. 


IJ 

1.0 
.0 
.8 
.7 
.6 
.5 

A 

— 

— 

^~ 

\ 

/ 

/ 

\ 

/ 

\ 

, 

\ 

/ 

\ 

. 

, 

*' 

5£ 

—  ' 

12    2     4      6 


10     n     2     4      6     8     10   12 


nearly  uniform  during  the  night.  The  curve  in  Figure  316 
shows  this  diurnal  variation  in  the  force  of  the  wind,  the  figures 
in  the  vertical  line  indicating  the  pressure  in  pounds  per  square 
foot. 


272 


ELEMENTS    OF 


404.  The  Cause  of  Winds.  —  Movements  of  the  atmos- 
phere are  produced  either  by  the  unequal  pressure  of  the 
atmosphere  at  different  points,  or  by  the  unequal  specific 
gravity  of  different  portions  of  the  atmosphere. 

Surface  currents  will  always  set  mfrom  a  region  of  high 
pressure  towards  a  region  of  low  pressure. 

Unequal  specific  gravity  of  the  air  may  be  due  to 
inequalities  of  temperature  or  of  humidity. 

Suppose  the  surface  of  the  earth  in  the  neighborhood  of  C 
Fig.  3i7.  (Figure  317)   to  become   exces- 

sively heated.     The  air  above  C 
will  by  expansion  become  lighter 
than  the  surrounding  air.     This 
lighter  air  will  accordingly  rise, 
and  its  place  will  be  supplied  by 
an  inflow  along  the  surface  from 
every  side.     At   the    same   time 
the  heated  column,  rising  above 
_^^__     the  surrounding  atmosphere,  gives 
rise  to  an  outflow  at  the  top.     At 
a  certain  distance  from  the  heated  column  there  will  be  descend- 
ing currents  to  supply  the  place  of  the  air  which  is  flowing  in 
Fi      ig  towards  the  heated  region 

at  the  surface  of  the  earth. 
The  system  of  currents 
that  would  be  developed 
on  every  side  of  an  exces- 
sively heated  region  is 
shown  in  Figure  318,  the 
arrows  indicating  the  direction  of  the  currents.  A  system  of 
currents  in  just  the  opposite  direction  would  be  developed  on 
every  side  of  an  excessively  cold  region. 

The  specific  gravity  of  the  vapor  of  water  is  only  about  two 
thirds  that  of  dry  air.  As  it  takes  time  for  the  vapor  to  diffuse 
itself  into  the  atmosphere,  an  excess  ofc  aqueous  vapor  tends  to 
produce  a  region  of  low  specific  gravity,  and  so  to  develop  a 
system  of  currents  similar  to  those  developed  by  a  region  of 
high  temperature. 


NATURAL    PHILOSOPHY.  273 

405.  The  Direction  of  the  Winds  modified  by  the  Rotation 
of  the  Earth. — The  earth's  rotation  from  west  to  east  in 
24  hours  is  on  an  axis  perpendicular  to  its  equator.     Every 
point  on  the  earth's  surface  is  carried  around  in  the  same 
time,  but  points  near  the  equator  describe  longer  paths, 
and   hence  must  move  with   greater  velocity  than   those 
near  the  poles.     The  velocity  of  rotation  at  the  surface  is 
greatest  at  the  equator  and  decreases  towards  the  poles. 
At  the  equator  it  is  1036  miles  per  hour;  15°  from  the 
equator  it  is  1000  miles  per  hour;  30°  from  the  equator, 
897  miles ;  45°  from  the  equator,  732  miles ;  60°  from  the 
equator,  518  miles;  75°  from  the  equator,  268  miles. 

If  a  mass  of  quiescent  air  from  parallel  30°  were  sud- 
denly transported  to  parallel  15°,  it  would  have  an  easterly 
motion  of  103  miles  an  hour  less  than  that  of  the  parallel 
arrived  at.  It  would  therefore  seem  to  be  moving  over 
the  surface  of  the  earth  westward  at  the  rate  of  103  miles 
an  hour.  Of  course  it  would  really  be  the  surface  of  the 
earth  which  would  be  moving  under  it  eastward  at  that 
rate.  The  effect  upon  bodies  on  the  surface  of  the 
earth  would  be  the  same  as  if  the  earth  was  stationary, 
and  the  wind  blowing  over  it  to  the  west  at  the  above 
rate. 

If,  on  the  other  hand,  a  mass  of  quiescent  air  were  sud- 
denly transported  from  parallel  15°  to  parallel  30°,  it  would 
have  an  easterly  motion  of  103  miles  an  hour  greater  than 
the  parallel  arrived  at. 

In  general,  any  wind  blowing  towards  the  equator  is 
deflected  towards  the  west  by  the  rotation  of  the  earth,  so 
as  to  make  it  an  easterly  wind  ;  and  any  wind  blowing/hw 
the  equator  is  deflected  towards  the  east  by  the  rotation  of 
the  earth,  so  as  to  make  it  a  westerly  wind. 

406.  Systems  of  Winds.  — There  are  three  great  systems 
of    winds   upon   the   globe,   namely,   the  trade-winds,  the 
middle-latitude  winds,  and  the  polar  winds. 

18 


274 


ELEMENTS    OF 


407.  Trade -Winds.  —  There   is   a  belt   of   excessively 
heated  air  surrounding  the  earth  within  the  tropics.     This 
heated  air  develops  a  system  of  currents  on  each  side  of 
it,  similar  to  those  described  in  section  404.     Surface  cur- 
rents set  in  towards  the  equator  from  the  north  and  the 
south,  and  upper  currents  from  the  equator  towards  the 
north  and  the  south.     The  rotation  of  the  earth  deflects 
the  surface  currents  towards  the  west,  so  as  to  make  them 
easterly  winds ;  and  the  upper  currents  towards  the  east,  so 
as  to  make  them  westerly  winds.     The  surface  wind  north 
of  the  equator  becomes  a  northeast  wind,  and  that  south 
of  the  equator  a  southeast  wind.     These  winds  are  called 
trade-winds,  from  the  service  they  render  to  commerce. 

408.  Cause  of  the  High  Barometer  near  the  Parallel  of  32°. 
—  As  the  upper  equatorial  currents  move  towards  the  poles 
they  tend  to  increase  the  pressure  of  the  atmosphere  towards 
the  north  and  the  south  ;  for  since  the  meridians  converge  as 
we  proceed  from  the  equator  towards  the  poles,  the  air  as  it 
moves  towards  the  poles  must  increase  in  depth,  and  so  produce 
a  greater  pressure  at  the  surface.     This  increased  pressure  of 
the  air  in  middle  latitudes  arrests  the  further  progress  of  the 
polar  current,  and  a  calm  ensues.     The  upper  air  descends  to 
the  earth's  surface,  and  joins  the  surface  current  towards  the 
equator,  where  it  again  ascends,  and  thus  maintains  a  perpetual 
circulation. 

409.  The  Middle- Latitude  Winds. — The  high   pressure 
near  the  parallel  of  32°  gives  rise  to  surface  currents  from 
the  equator  towards  the  poles,  and  to  upper  currents  from  the 
poles  towards  the  equator.      The  surface  currents   are  de- 
flected by  the  rotation  of  the  earth  towards  the  east,  so  as  to 

make  them  westerly  winds  ;  and  the  upper  currents  towards 
the  ivest,  so  as  to  make  them  easterly  winds.  These  surface 
currents  are  the  prevailing  winds  of  the  middle  latitudes. 
In  the  northern  hemisphere  they  blow  from  a  point  a  little 
south  of  west,  and  in  the  southern  hemisphere  from  a 
point  a  little  north  of  west.  Throughout  the  middle  lati- 


NATURAL    PHILOSOPHY. 


275 


tudes  of  the  United  States  the  average  direction  of  the 
wind  is  10°  south  of  west;  and  the  easterly  winds  are  to 
the  westerly  as  2  to  5.  In  corresponding  latitudes  in  the 
southern  hemisphere  the  prevalent  direction  of  the  surface 
winds  is  17°  north  of  west;  and  the  easterly  winds  are  to 
the  westerly  as  i  to  5. 

410.  The  Polar  Winds.  —  The  extreme  cold  of  the  polar 
regions  produces  the  opposite  effect  to  that  of  the  extreme 
heat  of  the  tropics.  It  produces  great  density  of  air,  and 
develops  surface  currents  from  the  poles  towards  the  equator ; 
and  upper  currents  in  the  opposite  direction.  These  currents 
are  deflected  by  the  rotation  of  the  earth,  as  in  all  other  cases. 
The  polar  and  middle-latitude  winds  encounter  each  other 
near  the  parallel  of  60°. 

Fig.  319- 

N 


The  three  systems  of  surface  winds  are  shown  in  Figure 
319,  the  arrows  indicating  the  direction  of  the  wind  in 
each  belt.  Figure  320  shows  the  complete  circulation  of 
the  atmosphere. 

411.  Monsoons.  —  During  the  summer  months  the  surface 
of  the  land  becomes  heated  to  a  higher  temperature  than 


276 


ELEMENTS    OF 


that  of  the  surrounding  water,  while  during  winter  it  becomes 
cooled  to  a  lower  temperature  (391).     Hence  during  the 
Fig.  320.  summer   months   there    is    a    ten- 

dency to  develop  surface  winds 
from  the  oceans  to  the  continents, 
and  in  the  opposite  direction  during 
the  winter  months.  This  tenden- 
cy may  either  give  rise  to  winds 
in  the  direction  in  which  it  acts, 
or  merely  modify  the  direction  and 
force  of  the  prevailing  winds. 

In  the  former  case  we  have 
what  are  called  monsoons,  that  is, 
winds  which  blow  during  the  sum- 
mer months  from  the  water  to  the 
land,  and  during  the  winter  months 
from  the  land  to  the  water.  The 
most  marked  monsoons  on  the 
globe  are  those  on  the  south  coast 
of  Asia,  in  the  region  of  the  northeast  trades.  The  ten- 
dency of  the  unequal  heating  of  the  continent  of  Asia  and 
of  the  Indian  Ocean  during  the  winter  months  is  to  produce 
a  wind  in  the  direction  of  the  trade-wind,  and  in  the 
summer  months  in  the  opposite  direction.  The  winter 
monsoon  adds  to  the  force  of  the  trade-wind,  while  the 
summer  monsoon  overbalances  the  trade,  and  produces 
a  wind  in  the  opposite  direction. 

412.  Land  and  Sea  Breezes,  —  During  the  day  the  surface  of 
the  land  becomes  hotter  than  that  of  the  neighboring  water,  and 
at  night  cooler.  There  is,  therefore,  a  general  tendency  for  the 
wind  to  blow  from  the  water  to  the  land  during  the  day,  and 
from  the  land  to  the  water  at  night.  When  this  tendency  is 
strong  enough  to  produce  a  wind  in  the  direction  in  which  it 
acts,  we  have  what  are  called  land  and  sea  breezes,  or  winds 
blowing  from  the  sea  during  the  heat  of  the  day,  and  from  the 
land  during  the  cool  of  the  night.  These  winds  are  strongest 
on  islands  in  tropical  regions. 


NATURAL    PHILOSOPHY.  277 

^      • 

V. 

CONDENSATION    IN   THE   ATMOSPHERE. 
A.    DEW  AND  HOAR-FROST. 

413.  Origin  of  Dew.  —  All  bodies  on  the  surface  of  the 
earth  are  radiating  heat  to  the  sky,  and  when  they  thus 
part  with  heat  faster  than  they  receive  it,  their  temperature 
falls  below  that  of  the  surrounding  air.     When  the  sun  is 
above  the  horizon,  they  generally  receive  heat  faster  than 
they  part  with  it  by  radiation,  but  at  night  they  usually 
radiate  heat  faster  than  they  receive  it. 

When  the  blades  of  grass,  leaves  of  plants,  and  other 
objects  on  the  surface  of  the  earth  become  cooled  by  radi- 
ation below  the  dew-point  of  the  atmosphere,  they  condense 
upon  themselves  a  portion  of  the  atmospheric  moisture  in  the 
form  of  dew.  The  greatest  amount  of  dew  is  deposited 
upon  the  substances  whose  temperature  becomes  the  low- 
est. Dew  does  not  fall  from  the  sky  like  rain,  but  collects 
upon  those  bodies  which  are  cool  enough  to  condense  the 
vapor  in  the  air  in  contact  with  them.  A  pitcher  of  ice- 
water,  on  a  warm  summer's  day,  becomes  quickly  covered 
with  a  film  of  dew,  the  cold  surface  of  the  pitcher  con- 
densing the  vapor  from  the  layer  of  air  in  contact  with  it. 

414.  Circumstances  favorable  to  the  Formation  of  Dew. — 
Anything  which  favors  the  loss  of  heat  by  radiation  is  favor- 
able to  the  formation  of  dew. 

A  cloudless  night  and  an  unobstructed  exposure  to  the  sky 
are  especially  favorable  to  the  formation  of  dew,  because 
they  allow  the  heat  radiated  by  bodies  to  escape  freely 
into  space.  A  cloudy  night  or  any  artificial  covering, 
however  slight,  prevents  the  formation  of  dew,  for  the 
clouds  or  coverings  reflect  back  the  heat  radiated  from 
the  earth,  and  so  keep  bodies  on  its  surface  from  cool- 
ing below  the  dew-point. 


2/8  ELEMENTS   OF 

A  slight  breeze  favors  the  formation  of  dew  by  renewing 
the  air  in  contact  with  the  surface  as  fast  as  it  deposits  its 
excess  of  vapor.  A  stiff  breeze,  however,  prevents  the 
formation  of  dew  by  allowing  no  layer  of  air  to  remain 
long  enough  in  contact  with  the  surface  of  a  body  to  be- 
come sufficiently  cooled  to  deposit  its  moisture.  There  is 
little  dew  on  windy  nights. 

A  moist  atmosphere  favors  the  formation  of  dew,  because 
the  more  moisture  in  the  air  the  less  the  reduction  of  tem- 
perature at  which  the  deposition  of  dew  will  begin.  Good 
radiators  and  bad  conductors  receive  the  greatest  amount  of 
dew.  The  temperature  of  their  surfaces  falls  rapidly  at 
night,  because  they  lose  heat  rapidly  by  radiation  and 
receive  it  slowly  by  conduction  from  their  interior  or 
from  the  earth  with  which  the  bodies  are  in  contact. 
Wool,  being  a  good  radiator  and  a  poor  conductor,  collects 
a  large  amount  of  dew  at  night,  while  a  plate  of  polished 
metal  will  receive  scarcely  any  at  all. 

415.  Formation  of  Hoar-Frost.  —  When  the  temperature 
of  the  surface  is  below  the  freezing-point,  the  moisture  of 
the  atmosphere  is  deposited  upon  it  in  the  solid  state,  as 
frost.     Hoar-frost  is  not  frozen  dew,  but  frozen  vapor,  that 
is,    vapor   deposited    in   the   solid   form   without   passing 
through  the  liquid  state. 

Since  the  leaves  of  plants  sometimes  become  cooled  by  radi- 
ation several  degrees  below  the  air  a  few  feet  from  them,  there 
may  be  a  frost  when  the  thermometer  indicates  a  temperature 
several  degrees  above  the  freezing-point.  There  is  not,  how- 
ever, likely  to  be  a  frost  unless  the  temperature  of  the  dew-point 
is  below  32°.  The  temperature  of  the  surface  will  not  fall  much 
below  the  dew-point,  because  of  the  heat  which  is  liberated  on 
the  deposition  of  the  dew. 

416.  Frost  in   Valleys.  —  There    is    often  sufficient  frost  in 
valleys  and  up  to  a  certain  height  on  the  hillsides  to  kill  plants, 
while  higher  up  there  is  no  frost  at  all.     As  the  air  on  the  hill- 
sides is  cooled  by  contact  with  the  cold  surface,   it  gradually 


NATURAL   PHILOSOPHY.  279 

settles  into  the  valley,  becoming  cooler  and  cooler  by  contact 
with  the  surface  as  it  descends,  and  raising  the  warmer  air 
bodily  out  of  the  bottom  of  the  valley,  just  as  a  heavy  liquid 
will  raise  a  lighter  one  by  flowing  under  it. 

B.   FOG  AND  MIST. 

417.  Origin  of  Fog.  —  The  watery  vapor  of  the  atmos- 
phere is  transparent,  but  when  from  any  cause  a  portion 
of  the  atmosphere  becomes  cooled  below  the  dew-point,  a 
part  of  the  vapor  becomes  condensed  into  minute  drops  of 
water  which  float  in  the  atmosphere.      The  partially  con- 
densed vapor  becomes  visible  as  a  mist  or  cloud.     When 
the  condensation  takes  place  near  the  surface  of  the  earth  it 
gives  rise  to  &fog  or  mist. 

When  steam  rises  from  a  vessel  of  warm  water  and  mixes 
with  the  colder  air  above,  a  portion  of  the  vapor  is  condensed 
into  a  mist  which  is  often  improperly  called  steam.  Steam 
proper  is  a  gaseous  body,  while  mist  is  a  liquid  body. 

418.  Fogs  over  Rivers.  —  At  certain  seasons  of  the  year, 
and  especially  during  the  latter  part  of  the  summer,  fogs 
form   over  rivers  and  lakes  almost  every  clear  and  still 
night.     During  the  night  the  air  over  the  land  becomes 
cooler  than  the  water  of  the  lake  or  river,  and  as  the  vapor 
rises  from  the  water  it  is  partially  condensed  by  contact  with 
the  cooler  air  from  the  land,  and  gives  rise  to  a  fog  which 
floats  upon  the  surface  of    the  water.     Fogs   are   often 
formed  in  a  similar  manner  over  harbors  and  bays,  and 
these  fogs  are  frequently  drifted  inland  by  gentle  currents 
of  air. 

419.  Fogs  on  the  Breaking  up  of  Frost.  —  Extensive  fogs 
often  occur  in  midwinter  after  a  thaw  or  a  warm  rain.     In 
this  case  warm  and  moist  currents  of  air  become  chilled  in 
passing  over  the  cold  surface  of  the  frozen  ground,  and  a  part 
of  the   moisture  is  condensed   as  a   fog.     For   a  similar 
reason  icebergs  are  liable  to  be  enveloped  in  mist,  the  ice 


280  ELEMENTS   OF 

cooling  the  surrounding  air  sufficiently  to  condense  a  part 
of  its  moisture. 

420.  Fogs  on  the  Banks  of  Newfoundland.  —  Fogs  prevail 
along  the   northern  side  of  the  Gulf   Stream,  the  warm   and 
moist  air  over  the  Gulf  Stream  being  chilled  by  contact  with 
the  colder  air  from  the  water  on  the  north.     These  fogs  are 
especially  prevalent  over  the  Banks  of  Newfoundland.     They 
occur  every  month  of  the  year,  but  are  especially  frequent  in 
the  summer,  when  the  Banks  are  enveloped  in  fog  nearly  half 
of  the  time.     The  shallow  Banks  compel  the  cold  arctic  current 
at  the  bottom  of  the  ocean  to  come  to  the  surface,  and  the  cold 
water  thus  brought  to  the  surface  chills  the  air  laden  with  mois- 
ture from  the  Gulf  Stream. 

421.  Mist  on  the  Tops  of  Mountains.  —  The  tops  of  moun- 
tains are  liable  to  be  enveloped  in  mist.     The  mountains  compel 
the  warm  currents  of  air  to  rise  to  pass  over  them.     As  these 
currents  rise  they  become  chilled  partially  by  expansion  (204), 
and  partially  by  contact  with  the  cold  surface  of   the   moun- 
tains.    When  the  air  is  chilled  below  its  dew-point,  a  mist  is 
formed,  which  is  again  dissipated  as  the  air  passes  down  into 
warmer  regions  on  the  other  side  of  the  mountains. 

422.  How  Fog  is  sustained  in  the  Air.  — The  particles 
of  fog  are  sustained  in  the  air  in  the  same  manner  as  a 
cloud  of  dust.    The  dust  remains  for  a  long  time  suspended 
in   the   air,  although  each  particle  may  consist  of  matter 
two  thousand  times  as  dense  as  the  air  in  which  it  floats. 
When  the  air  is  perfectly  tranquil,  these  particles  do  indeed 
fall,  but  their  descent  is  so  slow  that  their  motion  is  per- 
ceptible only  after  a  considerable  interval  of  time. 

423.  The  Indian  Summer.  —  At  certain  seasons  of  the  year 
there  occurs  what  is   called  a  dry  fog.     In  the  United  States 
this  frequently  occurs  in  November,  or  the  latter  part  of  Octo- 
ber, and  this  period  is  commonly  known  as  the  Indian  Summer. 
It  is  characterized  by  a  hazy  atmosphere,  a  redness  of  the  sky, 
absence  of  rain,  and  a  mild  temperature.     This  appears  to  re- 
sult from  a  dry  and  stagnant  state  of  the  atmosphere,  during 
which  the  air  becomes  filled  with  dust  and  smoke  from  numer- 


NATURAL   PHILOSOPHY.  281 

ous  fires.  A  heavy  rain  washes  out  these  impurities  and  clears 
the  sky.  Long  periods  of  drought  in  summer  are  characterized 
by  a  like  condition  of  the  atmosphere. 

C.   CLOUDS  AND  RAIN. 

424.  Natufe  and  Formation  of  Clouds.  —  A  cloud  differs 
from  a  fog  simply  in  its  elevation  above  the  earth.     A  fog 
might  be  defined  as  a  cloud  resting  on  the  earth  ;  and  a  cloud, 
as  a  fog  floating  in  the  air. 

Clouds  are  formed  whenever  a  mass  of  air  away  from  the 
earth's  surface  is  cooled  below  its  dew-point.  This  cooling 
may  be  effected  in  various  ways.  A  cold  wind  may  pene- 
trate a  mass  of  warm  air  and  cool  it  below  its  dew-point, 
or  a  warm  moist  wind  may  be  thus  cooled  by  penetrating 
a  mass  of  cold  air.  Ascending  currents  of  air  are  always 
cooled  by  expansion  (204),  and  are  very  likely  to  give  rise 
to  clouds. 

425.  Clouds  on  the  Summits  of  Mountains.  —  The  summits 
of  high  mountains  are  usually  enveloped  in  clouds  even  when 
the  rest  of  the  sky  is  clear.     An  interposed  mountain  forces  a 
horizontal  wind  up  to  an  unusual  height  where  the  temperature 
is  low.     When  the  temperature  of  the  ascending  current  reaches 
its  dew-point,  a  portion  of 

its  moisture  is  condensed 
as  a  cloud.  Let  ABC 
(Figure  321)  be  a  mountain 
interposed  in  the  path  of 
a  horizontal  current.  The 
current  will  be  forced  up- 
ward, and  made  to  glide 
along  the  side  of  the  moun- 
tain. Let  D  E  represent  the  elevation  at  which  the  temperature 
of  the  ascending  current  will  just  reach  its  dew-point.  As  soon 
as  the  current  passes  above  this  line  its  vapor  will  be  partially 
condensed  so  as  to  form  a  cloud,  which  will  envelop  the  summit 
of  the  mountain.  As  soon  as  the  current  passes  below  the  line 
D  E  on  the  other  side  of  the  mountain,  its  temperature  again 


282 


ELEMENTS   OF 


rises  above  its  dew-point,  and  the  cloud  is  redissolved.  The 
cloud  is  drifted  by  the  wind,  but  is  not  blown  away  from  the 
mountain  because,  as  fast  as  it  moves  forward,  a  new  cloud  is 
formed  behind  it.  Although  the  cloud  on  the  mountain  appears 
stationary,  the  particles  which  compose  it  are  continually 
changing. 

Even  in  tolerably  fevel  countries,  the  sky  does  not  become 
overcast  solely  by  clouds  drifted  by  the  wind  from  places  beyond 
the  horizon.  The  clouds  are  very  often  formed  in  sight  of  the 
observer.  So  too  the  sky  often  clears,  not  because  the  clouds 
are  drifted  off  by  the  wind,  but  because  they  are  dissipated  by 
the  increasing  heat  of  the  air. 

Fig.  322. 


426.  The  Classification  of  Clouds.  —  The  four  chief  va- 
rieties of  clouds  are  the  cirrus^  the  cumulus,  the  stratus, 
and  the  nimbus. 

The  cirrus  cloud  consists  of  long,  slender  filaments,  either 
parallel  or  diverging,  and  often  resembling  a  lock  of  cotton 
whose  fibres  are  electrified  so  as  to  repel  one  another. 
These  clouds  have  the  least  density,  the  greatest  elevation, 
and  the  greatest  variety  of  form.  They  are  generally  the 
first  to  appear  after  a  period  of  perfectly  clear  weather. 
They  are  believed  to  be  composed  of  spiculae  of  ice  or 
flakes  of  snow  floating  at  a  great  height  in  the  air.  At  the 
height  at  which  they  prevail  the  temperature  of  the  air  is 
below  32°  even  in  midsummer  (Figure  322). 


NATURAL   PHILOSOPHY.  283 

The  cumulus  cloud  usually  consists  of  a  rounded  mass, 
rising  from  a  horizontal  base.  It  is  much  denser  than  the 
cirrus,  and  is  formed  in  the  lower  regions  of  the  atmos- 
phere. In  fair  weather  it  often  forms  a  few  hours  after 
sunrise,  increases  until  the  hottest  part  of  the  day,  and 
disappears  about  sunset.  We  often  see  near  the  horizon 
large  masses  of  this  cloud  which  resemble  mountains  cov- 
ered with  snow. 

The  rounded  top  of  the  cumulus  is  due  to  the  mode  of 
its  formation.  When  the  surface  of  the  earth  is  heated  by 
the  rays  of  the  sun,  currents  of  warm  air  ascend,  and  at  a 
certain  height  a  portion  of  their  vapor  is  condensed  into 
cloud  ;  and  since  the  upward  motion  is  greatest  under  the 
centre  of  the  cloud,  the  vapor  is  there  carried  up  to  the 
greatest  height  (Figure  323). 

Fig-  323 


The  stratus  cloud  is  a  widely  extended  horizontal  sheet, 
often  covering  the  sky  with  a  nearly  uniform  veil.  It  is 
the  lowest  of  the  clouds,  and  sometimes  descends  to  the 
surface  of  the  earth  (Figure  324). 

The  nimbus  is  the  well-known  rain-cloud,  consisting  of 
a  combination  of  cirrus,  cumulus,  and  stratus  clouds 
(Figure  325). 

427.    T/ie  Height  and  Thickness  of  Clouds.  —  The  height 


2-84 


ELEMENTS    OF 


of  clouds  is  very  variable.  The  stratus  cloud  sometimes 
descends  to  the  surface  of  the  earth.  In  pleasant  weather 
the  under  surface  of  the  cumulus  cloud  is  from  3000  to 
5000  feet  high.  Cirrus  clouds  are  never  seen  below  the 
summit  of  Mont  Blanc. 

Fig.  324. 


Clouds  are  not  usually  more  than  half  a  mile  thick, 
though  cumulus  clouds  sometimes  attain  a  thickness  of 
3  or  4  miles. 

Fig.  325- 


428.  How  Clouds  are  sustained  in  the  Atmosphere. — 
Since  clouds  are  composed  of  particles  heavier  than  air, 
they  must  be  slowly  sinking.  They  do  not  ultimately  fall 
to  the  earth  in  pleasant  weather,  because,  as  they  sink, 


NATURAL   PHILOSOPHY.  285 

they  encounter  warmer  layers  of  air  which  are  not  saturated 
with  vapor.  The  cloud  is  therefore  dissipated  at  the  bottom 
as  fast  as  it  falls,  while  it  is  at  the  same  time  renewed  at 
the  top  by  the  condensation  of  vapor  carried  up  by  ascending 
currents. 

429.  Origin  of  Rain.  —  Rain  has  the  same  origin  as 
clouds.      When  the  condensation  takes  place  slowly,  clouds 
only  are  formed;  but  when  it  takes  place  with  sufficient  rapid- 
ity, rain  is  also  formed.     To  produce  an  abundant  rain,  the 
air  must  be   suddenly  cooled  below  the  dew-point.     The 
most  effective  way  to  accomplish  this  is  to  force  the  air  up 
a  mile  or  two  above  the  surface  of  the  earth.     Were  a  mass 
of  air  raised  two  miles  from  the  surface  of  the  earth,  its 
temperature  would  fall  about  35°,  partly  from  the  chilling 
effects  of  expansion  and  partly  from  the  coldness  of  the 
space  into  which  the  air  would  be  transported.     Were  the 
air  of  the  surface   of  the  earth  forced  up  to  this  height, 
most  of  its  vapor  would  be  condensed.     The  air  may  be 
forced  upward  by  the  interposition  of  a  mountain  range 
in  the  path  of  a  current  of  air,  or  by  the  meeting  of  two 
opposing  currents.    Hence  mountain  ranges  are  very  efficient 
condensers  of  the  atmospheric  Taper.     The  heaviest  rainfall 
on  the  globe  occurs  where  the  prevailing  wind  is  from  the 
ocean,  and  is  obliged  to  pass  over  a  high  mountain  range 
on  its  way  to  the  interior  of  the  continent.     On  the  she!« 
tered  side  of  such  ranges  there  are  often  desert  regions. 

430.  The  Amount  of  Ram  in  Different  Latitudes.  —  The 
average   rainfall   is  greatest  at  the  equator,   and   decreases 
towards  the  poles.     The  annual  rainfall  at  the  equator  is 
104  inches;  in   latitude   20°,  70  inches;  in  latitude  30°, 
40  inches ;  and  in  latitude  60°,  20  inches. 

431.  Origin  of  Snow.  —  Snow  bears  the  same  relation 
to  rain  that  hoar-frost  does  to  dew.     When  the  vapor  of 
the  atmosphere  is  precipitated  at  a  very  low  temperature, 
it  at  once  assumes  the  solid  state,  usually  in  the  form  of 


286  ELEMENTS   OF 

minute  crystals,  which  attach  themselves  to  each  other  and 
form  snow-flakes,  which  fall  slowly  to  the  earth.  Snow- 
flakes  present  a  great  variety  of  forms,  some  of  which  are 
shown  in  Figure  326. 

Fig.  326. 


432.   Hail.  —  Large   hail   seldom   if   ever  falls   except 
during  thunder-storms.     It  very  rarely  follows  rain  which 
Fig.  327^  has  continued  for  some 

time.  The  hail  covers 
a  much  smaller  area  than 
the  rain-storm,  and  usu- 
ally continues  at  the 
same  place  for  only  five 
or  ten  minutes.  Hail- 
stones are  of  all  sizes, 
from  that  of  small  shot 
to  that  of  a  turkey's  egg,  and  of  every  variety  of  shape. 


NATURAL   PHILOSOPHY.  287 

One  of  very  irregular  form  is  shown  in  Figure  327.  The 
centre  of  large  hailstones  usually  consists  of  hardened 
snow,  and  this  is  surrounded  by  a  layer  of  transparent 
ice.  Sometimes  we  find  several  alternate  layers  of 
opaque  snow  and  transparent  ice.  Figure  328  shows 

Fig.32s.          the    section    of    a   hail-  Fig.329. 

stone     whose      external 

form  is  given  in  Figure 
329- 

432a.  Origin  of  Hail.  — 
The  formation  of  hail  is 
invariably  attended  by  two 
distinct  currents  of  air,  one  of  which  displaces  the  other  with 
great  violence.  The  current  of  air  which  precedes  the  approach 
of  a  hail-storm  is  extremely  hot,  and  highly  charged  with  mois- 
ture ;  and  that  which  succeeds  the  fall  of  hail  has,  an  icy  chill- 
ness.  The  warm  and  humid  air  is  displaced  by  the  cold  current, 
and  is  thus  forced  up  to  a  great  height,  by  which  means  its  vapor 
is  suddenly  condensed.  Upon  the  front  of  the  hail-cloqd  this 
condensed  vapor  exists  in  the  form  of  water,  whose  temperature 
is  near  32°.  In  the  interior  of  the  cloud  the  vapor  is  precipi- 
tated in  the  form  of  snow,  whose  temperature  may  be  as  low  as 
20°. 

Observations  on  mountains  have  shown  that,  on  the  front  of 
the  hail-cloud  there  is  a  violent  whirling  motion  about  a  horizon- 
tal axis.  This  causes  the  snow  to  collect  in  small  balls,  each  of 
which  forms  the  nucleus  of  a  hailstone.  The  snow-ball  is  forced 
into  the  warm  current,  where  it  receives  a  layer  of  water,  which 
is  congealed  by  the  nucleus,  thus  rendering  the  snowy  centre 
more  compact,  and  adding  a  shell  of  transparent  ice.  By  the 
whirling  motion,  the  hailstone  is  then  hurled  into  the  snow- 
cloud,  where  it  receives  a  layer  of  snow,  and  again  becomes 
thoroughly  chilled.  Thence  it  escapes  again  into  the  water- 
cloud,  and  is  covered  with  a  layer  of  water,  which  is  frozen  by 
the  cold  of  the  nucleus.  Thus  it  is  plunged  alternately  into  the 
snow-cloud  and  the  water-cloud,  while  each  alternation  furnishes 
a  layer  of  spongy  ice  and  a  layer  of  transparent  ice.  Hence 


2.88  ELEMENTS    OF 

the  stone  grows  rapidly,  and  in  a  few  minutes  becomes  a  ball 
three  or  four  inches  in  diameter. 

The  hailstones  are  sustained  in  the  air  by  the  violent  upward 
motion  caused  by  the  cold  current  displacing  the  warm  one.  A 
sphere  of  ice  two  inches  in  diameter,  falling  through  a  tranquil 
atmosphere,  soon  acquires  a  velocity  of  90  feet  per  second.  A 
hailstone  of  irregular  shape  would  experience  more  resistance 
than  a  sphere,  and  would  acquire  less  velocity,  but  it  would  still 
fall  from  a  height  of  18,000  feet  in  about  three  minutes,  which 
time  is  too  small  to  allow  the  formation  of  masses  of  ice  weigh- 
ing a  pound.  An  upward  current  of  air,  rising  with  a  velocity 
of  90  feet  per  second,  would  sustain  a  sphere  of  ice  two  inches 
in  diameter,  and  would  greatly  reduce  the  velocity  of  stones  of 
larger  size. 

D.    STORMS. 

433.  Origin  of  Storms.  — Any  violent  and  extensive  com- 
motion of  the  atmosphere  is  called  a  storm.  Such  commo- 
tions are  usually  attended  by  a  fall  of  rain,  snow,  or  hail, 
but  the  storm  often  extends  beyond  the  area  of  snow  or 
rain,  and  even  beyond  the  area  of  clouds. 

Storms  are  caused  by  a  strong  and  extensive  upward  motion 
of  the  air.  Since  the  air  is  heated  by  contact  with  the  earth, 
and  by  absorption  of  solar  and  terrestrial  radiations  by  the 
watery  vapor  it  holds^  (381)  it  becomes  heated  chiefly  at  the 
bottom,  the  watery  vapor  existing  chiefly  in  the  lower  layers. 
An  excessive  heating  of  a  mass  of  air  at  the  surface  of  the 
earth  gives  rise  to  a  system  of  currents  such  as  has  been  already 

described  (404).     A  verti- 

Fis-  330.  cai  section  of  this  system 

of  currents  is  shown  in 
Figure  330  ;  a  horizontal 
section  at  the  bottom,  in 
Figure  331  ;  and  a  hori- 
zontal section  at  the  top, 
in  Figure  332. 

As  the  air  in  the  centre  of  the  area  rises,  it  is  cooled  by 
expansion  at  the  rate  of  about  38°  for  every  two  miles  of 


NATURAL    PHILOSOPHY. 


289 


ascent.  The  height  to  which  the  air  will  have  to  rise  to  be 
cooled  to  its  dew-point  depends  upon  the  difference  between 
,he  dew-point  and  the  temperature  of  the  air.  As  soon  as 
the  cloud  begins  to  form,  the  latent  heat  of  the  vapor  is  set 

Fig.  331- 


Fig.  332- 


free  (139).  A  rainfall  of  one  inch  precipitates  over  two  million 
cubic  feet  of  water  upon  one  square  mile  of  surface,  and  lib- 
erates as  much  heat  as  it  would  take  to  evaporate  two  million 
cubic  feet  of  water.  It  takes  over  60,000  units  of  heat  (196) 
to  evaporate  one  cubic  foot  of 
water.  The  heat  thus  liberated 
warms  the  air  in  the  region  in 
which  the  condensation  occurs, 
and  causes  the  mass  of  air  to  rise 
still  higher,  so  that  more  of  its 
vapor  is  condensed  and  more  heat 
is  liberated. 

The  expansion  of  the  column  of 
air  ascending  in  the  centre  of  a 
storm,  especially  after  heat  begins 
to  be  liberated  by  the  condensation, 
causes  the  air  to  spread  out  in  all  directions  above,  making  a 
barometer  under  the  centre  of  the  cloud  fall  below  its  mean 
height,  and  one  beyond  the  limits  of  the  cloud  rise  above  its 
mean  height.  Near  the  limits  of  the  cloud  the  air,  being  heavier, 
sinks  downward,  and  a  portion  of  it  flows  along  the  surface 
towards  the  centre  of  the  ascending  column,  while  another  por- 
tion flows  along  the  surface  in  the  opposite  direction,  producing 

'9 


290  ELEMENTS    OF 

a  gentle  breeze  away  from  the  cloud.  The  air  spreads  out  more 
rapidly  above  than  it  runs  in  below,  and  the  storm  tends  to 
increase  in  diameter.  Storms  often  extend  with  great  rapidity 
till  they  cover  an  area  of  more  than  a  thousand  miles  in  di- 
ameter. 

434.  The  Development  and  Motion  of  Storms.  —  Storms 
begin  gradually,  and  are  usually  a  day  or  two  in  attaining 
their  greatest  violence.  After  a  day  or  two  longer  their 
violence  again  decreases,  and  at  length  they  disappear  or 
are  merged  into  other  storms.  A  storm  occasionally  lasts 
one  or  two  weeks,  but  usually  only  a  few  days.  It  some- 
times remains  nearly  stationary  for  a  day  or  two,  but  it 
usually  moves  eastward  about  600  miles  a  day.  * 

The  average  direction  of  storms  across  the  United  States 
is  a  little  north  of  east,  being  almost  exactly  east  during 
the  summer. 

The  average  velocity  of  a  storm  is  twenty-six  miles  an 
hour,  being  twenty-one  in  the  summer  and  thirty  in  the 
winter.  They  occasionally  move  at  the  rate  of  fifty  miles 
an  hour,  and  sometimes  remain  almost  stationary  for  a  day 
or  two. 

The  direction  in  which  a  storm  moves  is  entirely  distinct  from 
that  of  the  wind  which  accompanies  -it.  While  the  storm  moves 
steadily  eastward,  the  wind  has  every  possible  direction  at 
places  within  the  limits  of  the  storm.  At  places  on  the  north 
side  of  the  centre  of  the  storm,  the  wind  usually  sets  in  from 
the  northeast  as  the  storm  approaches,  and  veers  round  by  the 
north  to  the  northwest  as  the  storm  passes  over.  At  places  on 
the  south  side  of  the  centre,  the  wind  generally  sets  in  from  the 
southeast,  and  then  veers  round  by  the  south  to  the  southwest. 

Near  the  centre  of  a  great  storm  there  is  usually  a  lull  in  the 
wind,  and  sometimes  a  calm.  There  is  seldom  any  rain,  and 
the  clouds  often  break,  and  occasionally  there  is  a  clear  sky  for 
several  hours.  Soon  after  the  centre  of  the  storm  has  passed 
the  wind  changes  to  the  west,  and  there  is  a  heavy  fall  of  rain 
or  snow  of  comparatively  short  duration. 

The  winds  on  the  east  side  of  a  storm  are  propagated  in  a 


NATURAL    PHILOSOPHY. 


29I 


direction  opposite  to  that  in  which  they  blow.  That  is  to  say, 
they  are  propagated  eastward  while  they  blow  westward.  Winds 
propagated,  like  these,  in  the  opposite  direction  to  that  in  which 
they  blow  are  said  to  be  propagated  by  aspiration.  The  winds 
on  the  west  of  the  storm  are  propagated  in  the  same  direction 
as  that  in  which  they  blow.  Such  winds  are  said  to  be  propa- 
gated by  impulsion. 

435-  Cyclones.  —  The  inequalities  of  the  earth's  surface 
greatly  modify  the  direction  of  the  wind,  so  that  in  great  storms 
the  movements  of  the  atmosphere  often  seem  very  complex. 
Over  the  ocean  these  disturbing  causes  do  not  exist,  and  in 
violent  storms  the  movements  of  the  air  are  much  more  regular 
and  uniform.  The  motion  of  the  wind  is  generally  spirally 
inward  towards  the  centre  of  the  storm,  and  such  storms  are 
now  commonly  designated  by  the  term  cyclone.  These  storms 
prevail  in  the  neighbor- 
hood of  the  West  India 
Islands,  where  they  are 
known  as  hurricanes. 
They  are  also  common  in 
the  China  Sea  and  in  the 
Indian  Ocean. 

Cyclones  originate  near 
the  equatorial  limits  of  the 
trade-winds,  and  move 
northward  and  southward 
in  parabolic  paths,  as 
shown  in  Figure  333. 
The  small  arrows  indicate 

«9 

the  direction  of  the  circu- 
lation of  the  wind  in  the  cyclone  itself.     Tornadoes  are  very 
violent  storms,  caused  by  a  sudden  and  very  great  fall  of  pres- 
sure. 

436.  Predictions  founded  upon  the  Established  Laws  of 
Storms.  — "  The  laws  of  storms  are  now  so  well  understood 
that  we  can  predict  with  some  confidence  the  changes  which 
will  succeed  at  any  place  during  the  next  few  hours,  provided 
we  can  know  the  state  of  the  weather  throughout  the  surround- 
ing region  to  a  great  distance.  This  is  what  has  been  attempted 


292  ELEMENTS    OF 

since  1871  by  the  United  States  Signal  Service,  and  the  general 
accuracy  of  these  predictions  has  excited  considerable  surprise. 
Such  predictions  would  be  still  more  reliable  if  we  could  have 
information  respecting  the  various  meteorological  elements  from 
a  larger  portion  of  the  earth's  surface.  The  centre  of  a  large 
portion  of  our  storms  follows  nearly  the  northern  boundary  of 
the  United  States,  so  that  our  observations  inform  us  respecting 
only  one  half,  or  perhaps  less  than  one  half,  of  the  storm-area. 
Moreover,  storms  are  often  affected  by  changes  which  are  going 
on  in  very  distant  quarters.  An  area  of  unusually  high  barom- 
eter may  affect  the  course  of  a  storm  whose  centre  is  distant 
two  or  three  thousand  miles  ;  and  an  unusual  fall  of  rain  in  the 
equatorial  regions  may  cause  an  unusual  overflow  of  air  to  the 
middle  latitudes,  resulting  in  serious  disturbances  of  atmos- 
pheric pressure.  When  the  laws  of  storms  have  been  more 
precisely  defined,  and  telegraphic  reports  can  be  received  from 
a  more  extended  area,  we  shall  doubtless  be  able  to  predict 
coming  storms  with  greater  precision." 


VI. 


ELECTRICAL    PHENOMENA    OF    THE   ATMOS- 
PHERE. 

A.    ATMOSPHERIC  ELECTRICITY. 

437.  Electrical  Condition  of  the  Atmosphere.  —  The  atmos- 
phere is  almost  always  charged  with  electricity,  and  usually 
with  positive  electricity.  There  are,  however,  great  varia- 
tions in  the  intensity  of  the  charge,  and  clouds  are  fre- 
quently charged  with  negative  electricity. 

The  intensity  of  atmospheric  electricity  varies  regularly  with 
the  hour  of  the  day  and  with  the  season  of  the  year.  During 
the  day  it  is  least  intense  at  4  A.  M.  and  at  4  P.  M.,  and  most 
intense  at  10  A.  M.  and  at  10  p.  M.  It  is  least  intense  during 
the  summer  months  and  most  intense  during  the  winter  months. 
The  intensity  also  increases  with  the  altitude  above  the  surface 
of  the  earth. 


NATURAL    PHILOSOPHY.  293 

When  the  sky  is  covered  with  clouds  there  are  frequent 
changes  in  kind  as  well  as  in  intensity  of  electricity,  the  atmos- 
phere being  sometimes  positive  and  sometimes  negative.  It  is 
seldom  negative,  however,  except  when  rain  is  falling.  When 
snow  is  falling,  the  lower  layer  of  air  becomes  highly  charged 
with  electricity.  During  a  thunder-shower  the  electricity  of  the 
air  frequently  changes  in  two  or  three  minutes  from  positive  to 
negative,  and  back  to  positive  again,  and  sometimes  half  a  dozen 
of  these  changes  occur  during  a  single  shower. 

B.   LIGHTNING. 

438.  Lightning.  —  Two  clouds  having  opposite  electri- 
cities attract  each  other,  and  when  they  come  sufficiently 
near,    the  two  electricities  rush  towards  each  other  with  great 
violence.     This  phenomenon  is  called  lightning,  and  is  ac- 
companied by  an  explosive  noise  called  thunder. 

Since  clouds  are  very  imperfect  conductors,  when  the  elec- 
tricity of  one  part  of  a  cloud  is  discharged,  the  electricity  of  a 
distant  part  is  but  slightly  changed.  Thus,  A  single  discharge 
does  not  establish  a  complete  electrical  equilibrium  ;  but  there 
is  a  change  in  the  distribution  of  the  electricities  upon  the  sur- 
rounding clouds,  and  there  must  be  a  succession  of  discharges 
before  the  electricity  is  entirely  neutralized.  Hence  results  a 
succession  of  flashes  of  lightning  and  peals  of  thunder. 

A  cloud  charged  with  electricity  exerts  an  inductive  influence 
upon  the  earth's  surface  immediately  beneath  it,  decomposing 
its  natural  electricities,  repelling  electricity  of  the  same  kind, 
and  attracting  the  opposite  kind.  Accordingly  there  will  some- 
times be  a  discharge  of  electricity  from  /he  cloud  to  the  earth. 
This  charge  is  usually  received  by  the  most  elevated  objects, 
such  as  mountains,  hills,  trees,  spires,  high  buildings,  etc. 
Trees  are  particularly  exposed  to  strokes  of  lightning  on  ac- 
count of  their  elevation,  as  well  as  of  the  moisture  they  contain, 
which  renders  them  partial  conductors  of  electricity. 

439.  Lightning- Rods.  —  Buildings  may  be  protected  from 
injury  by  the  use  of  lightning-rods.     These   are  metallic 
rods  running  from  the  top  of  the  building  to  the  ground. 


294  ELEMENTS    OF 

The  rods  must  not  be  too  small,  and  their  parts  must  t»e 
well  connected  so  as  to  be  in  good  metallic  contact.  They 
should  run  well  into  the  earth  at  the  bottom,  and  be  care- 
fully pointed  at  the  top.  There  ought  to  be  several  sets 
of  points  on  the  top  of  the  building  connected  by  metallic 
rods  with  each  other  and  with  the  rod  that  runs  to  the 
ground  ;  and  if  the  building  is  at  all  large  there  ought  to 
be  several  rods  running  to  the  ground,  all  connected  to- 
gether by  metallic  rods.  If  the  building  has  a  metallic 
roof,  or  there  are  metallic  pipes  or  other  masses  of  metal 
in  the  interior,  these  should  all  be  carefully  connected  with 
the  rod.  The  points  facilitate  the  escape  of  the  electricity 
from  the  building  and  the  ground  around  it  when  these  are 
acted  upon  inductively  by  the  cloud.  Should  the  electric- 
ity be  developed  by  induction  more  rapidly  than  it  can 
escape  silently  from  the  points,  and  a  spark  discharge 
should  take  place,  the  rod  serves  as  the  path  of  least  re- 
sistance, and  the  discharge  will  take  this  path  rather  than 
pass  through  the  building. 

440.  Forms  of  Lightning.  —  Lightning  exhibits  a  variety 
of  forms,  which  have  been  designated  as  zigzag,  ball,  sheet, 
and  heat  lightning. 

Zigzag  lightning  presents  a  long,  irregular,  jagged  line 
of  light,  like  the  ordinary  spark  from  an  electrical  ma- 
chine (318).  This  zigzag  path  is  sometimes  four  or  five 
miles,  and  perhaps  even  ten  miles  in  length. 

Ball  lightning  appears  like  a  ball  of  fire,  and  is  usually 
accompanied  by  a  terrific  explosion.  It  probably  results 
from  a  charge  of  electricity  unusually  intense,  which  forces 
a  direct  instead  of  a  circuitous  passage  through  the  air. 

Sheet  lightning  is  a  diffuse  glare  of  light,  sometimes  illu- 
minating only  the  edges  of  a  cloud,  and  sometimes  spread- 
ing over  its  entire  surface.  This  may  be  sometimes  due  to 
distant  lightning  which  illumines  a  cloud,  while  the  direct 
flash  is  hidden  by  intervening  clouds.  Sometimes  it  may 


NATURAL    PHILOSOPHY.  295 

result  from  a  movement  of  electricity  in  the  interior  of  a 
cloud  which  is  a  very  imperfect  conductor,  producing  an 
illumination  analogous  to  that  observed  on  a  plate  of  moist 
glass  employed  in  discharging  an  electrical  machine. 

During  the  evenings  of  summer  the  horizon  is  some- 
times illumined  for  hours  by  flashes  of  light  unattended  by 
thunder.  This  is  called  heat  lightning,  and  is  sometimes 
due  to  the  reflection  from  the  atmosphere  of  the  lightning 
of  clouds  so  distant  that  the  thunder  cannot  be  heard. 
Sometimes,  however,  this  light  overspreads  the  entire 
heavens,  showing  that  the  electricity  of  the  clouds  escapes 
in  flashes  so  feeble  that  they  produce  no  audible  sound. 
This  may  occur  when  the  air  is  very  moist,  the  air  being 
then  a  tolerable  conductor,  and  offering  just  sufficient  re- 
sistance to  the  passage  of  the  electricity  to  develop  a  feeble 
light. 

441.  Thwider. — The  light  of  lightning  proceeds  from 
the  a:r,  which  is  heated  white-hot  along  the  line  of  discharge 
by  the  passage  of  the  electricity.  The  thunder  seems  to 
be  the  noise  produced  by  the  sudden  expansion  and  contraction 
of  this  heated  air. 

Sound  travels  only  1090  feet  a  second,  while  the  trans- 
mission of  light  is  nearly  instantaneous.  Hence  the  sound 
does  not  reach  the  ear  until  some  time  after  the  flash  is 
seen  (144).  By  observing  the  interval  between  the  flash 
and  the  report,  the  distance  of  the  point  of  discharge  can  be 
ascertained,  sound  travelling  a  mile  in  about  five  seconds. 
Thunder  is  seldom  heard  more  than  ten  miles  away. 

The  sound  is  produced  instantaneously  at  every  point  along 
the  line  of  the  flash,  but,  since  different  parts  of  the  flash  are 
usually  at  unequal  distances  from  the  observer,  the  sound  from 
different  points  will  reach  the  ear  in  slow  succession,  producing 
a  prolonged  peal  of  thunder.  The  prolonged  duration  of  some 
peals  of  thunder  is  in  part  due  to  echoes,  produced  by  reflection 
from  the  sides  of  mountains  or  from  clouds. 


296  ELEMENTS    OF 

The  variable  intensity  or  rolling  of  thunder  is  due  partly  to 
the  zigzag  course  of  the  discharge,  which  often  brings  several 
points  of  the  flash  equally  distant  from  the  observer  (the  sounds 
from  these  points  reach  the  ear  simultaneously,  and  so  pro- 
duce a  sound  of  double  and  triple  the  intensity)  ;  and  partly  to 
the  unequal  distance  of  different  parts  of  the  flash,  the  sound 
decreasing  in  intensity  as  the  square  of  the  distance  increases 
(143).  The  rolling  is  in  part  also  the  effect  of  echoes. 

Thunder  often  begins  with  a  rattling  sound,  followed  by  a 
loud  peal  of  variable  intensity,  and  ends  with  a  low  rattling 
sound.  This  may  be  due  to  a  discharge  like  that  represented 
in  Figure  334.  An  observer  at  E  would  first  hear  a  rattling 
sound  from  the  branches  A  C,  A  C',  etc.,  from  the  first  cloud 

Fig-  334- 


and  then  a-  loud  crash  of  variable  intensity  from  the  concen- 
trated discharge  between  A  and  B,  and  finally  a  rumbling  sound 
from  the  branches  B  D,  BD\  etc.,  of  the  distant  cloud,  the 
noise  being  feeble  on  account  of  the  great  distance. 

C.   THE  AURORA. 

442.  The  Polar  Light. — The  polar  light  is  a  luminous 
appearance  frequently  seen  near  the  horizon  as  a  diffused 
glow,  similar  to  that  of  the  dawn,  whence  it  has  received 
the  name  of  aurora. 

443.  Varieties  of  the  Aurora.  —  Auroras    exhibit   a  great 
variety  of  appearances,  but  they  may  be  generally  referred  to 
one  of  the  following  classes  :  — 


NATURAL    PHILOSOPHY. 


297 


1.  A  horizontal  light  like  the  morning  aurora  or  break  of 
day. 

2.  An  arch  of  light  somewhat  in  the  form  of  a  rainbow. 
This  arch  frequently  extends  entirely  across  the  heavens  from 
east  to  west,  and  cuts  the  magnetic  meridian  nearly  at  right 
angles.     It  does  not  long  remain  stationary,  but  frequently  rises 

Fig.  335- 


and  falls  ;  and  several  parallel  arches  are  often  seen  at  the  same 
time,  appearing  as  broad  belts  of  light,  stretching  from  the 
eastern  to  the  western  horizon  (Figure  335). 

Fig.  336. 


The  arches  sometimes  present  the  appearance  of  a  brilliant 
curtain  agitated  by  the  wind  (Figure  336). 

3.  Slender,  luminous  beams  or  columns,  well  defined,  and 
often  of  a  bright  light.  These  rise  to  heights  from  20°  or  30° 


298  ELEMENTS    OF 

up  to  90°  or  more,  sometimes,  though  rarely,  passing  the  zenith. 
Their  breadth  varies  from  a  quarter  of  a  degree  up  to  two  or 
three  degrees.  They  often  last  only  a  few  minutes,  but  some- 
times they  continue  a  quarter  or  half  of  an  hour,  or  even 
a  whole  hour.  Sometimes  they  remain  at  rest,  and  some- 
times they  have  a  quick  lateral  motion.  Their  light  is  com- 
monly of  a  pale  yellow,  sometimes  reddish,  occasionally  crimson, 
or  even  blood-red.  Sometimes  the  luminous  beams  are  inter- 
spersed with  dark  rays  resembling  dense  smoke.  Sometimes 
the  tops  of  the  beams  are  pointed  and  have  a  waving  motion. 

4.  Luminous  beams  sometimes  shoot  up  from  nearly  every 
part  of  the  horizon,  and  converge  to  a  point  a  little  south  of  the 
zenith,  forming  a  quivering  canopy  of  flame,  which  is  called  the 
corona.     The  sky  now  resembles  a  fiery  dome,  and  the  crown 
appears  to  rest  upon  variegated  fiery  pillars  frequently  traversed 
by  waves  or  flashes  of  light.     This  may  be  called  a  complete 
aurora,  and  comprehends  most  of  the  peculiarities  of  the  other 
varieties. 

5.  Waves  or  flashes  of  light.     The  luminous  beams  some- 
times appear  to  shake  with  a  tremulous  motion  ;  flashes  like 
waves  of  light  roll  up  towards  the  zenith,  and  sometimes  travel 
along  the  line  of  an  auroral  arch.     Sometimes  the  beams  have  a 
slow  lateral  motion  from  east  to  west,  and  sometimes  from  west 
to  east.     These  sudden  flashes  form  an  important  feature  of 
nearly  every  splendid  aurora. 

VII. 

OPTICAL   PHENOMENA   OF  THE   ATMOSPHERE. 
A.  REFRACTION. 

444.  Astronomical  Refraction.  —  When  a  ray  of  light 
from  a  star  or  other  heavenly  body  enters  the  atmosphere 
obliquely,  it  will  be  bent  downward,  or  towards  a  vertical 
line  drawn  from  the  point  of  contact  of  the  ray  with  the 
atmosphere  to  the  surface  of  the  earth  ;  and  as  the  air 
grows  denser  as  we  approach  the  earth,  the  ray  will  be 
bent  more  and  more  as  it  passes  through  the  atrnosphere 


NATURAL   PHILOSOPHY.  299 

from  layer  to  layer  (239).  As  we  always  see  the  body 
which  emits  the  ray  in  the  direction  of  the  ray  when  it 
enters  the  eye,  the  effect  of  this  refraction  will  be  to  make 
cuzry  heavenly  body  appear  farther  above  the  horizon  and 
nearer  the  zenith  than  it  really  is.  A  star  in  the  zenith  is 
not  displaced  by  refraction,  because  the  rays  from  it  enter 
the  air  perpendicularly,  and  therefore  without  bending. 
The  farther  a  star  is  from  the  zenith,  the  more  obliquely 
its  rays  enter  the  atmosphere,  and  the  greater  the  re- 
fraction. 

445.  Mirage.  —  Objects  within  the  atmosphere  are 
sometimes  displaced  or  made  to  appear  double  by  the  re- 
fraction of  the  air.  This  phenomenon  is  called  mirage. 

Fig-  337- 


446.  Mirage  upon  a  Desert.  —  Upon  a  hot  desert,  on  a 
still  day,  objects  are  often  seen  reflected  in  a  lower  stratum 
of  air  so  as  to  give  the  appearance  of  water  (Figure  337). 

The  layers  of  air  near  the  hot  sand  become  more  heated,  and 
consequently  rarer,  than  those  higher  up.  Hence  rays  coming 
from  any  object,  as  the  tree  (Figure  338),  would,  on  passing 


3°° 


ELEMENTS    OF 


downward,  be  entering  continually  rarer  and  rarer  layers  of  air. 
They  would  therefore  be  bent  upward  more  and  more,  till  they 
finally  meet  a  layer  at  an  angle  exceeding  the  limiting  angle,  and 
become  totally  reflected  (240).  This  total  reflection  of  the  rays 
causes  objects  to  be  mirrored  in  the  layers  of  air  as  in  the 
surface  of  water. 

Fig.  338- 


447.  Mirage  over  Water.  —  Objects  .at  a  distance  over 
water,  partially  or  entirely  below  the  horizon,  often  appear 
suspended  in  the  air,  sometimes  erect,  sometimes  inverted, 

and   sometimes  both    erect  and  inverted,  as 

shown  in  Figure  339. 

Fig.  340. 


Fig-  339- 


In  this  case  the  layers  of  air  near  the  cold  surface  of  the 
water  are  considerably  colder  and  denser  than  those  higher  up. 
Rays,  therefore,  which  pass  upward  from  an  object  are  contin- 
ually entering  rarer  layers  of  air,  and  are  therefore  bent  more 


NATURAL   PHILOSOPHY.  301 

and  more  downward,  as  shown  in  Figure  340.  If  the  rays  A  C 
and  B  D,  coming  from  the  top  and  bottom  of  the  object,  are 
totally  reflected  at  the  points  C  and  D,  they  will  cross  on  their 
way  to  the  eye,  and  cause  the  object  to  appear  elevated  and 
inverted  z\.  A'  B'.  If  the  rays  coming  from  the  top  and  bottom 
of  the  object  are  simply  bent  round  without  being  totally  re- 
flected, they  will  not  cross  before  entering  the  eye,  and  the  object 
will  appear  elevated  and  erect,  as  at  A"  B".  The  elevation  of 
an  object  by  refraction  without  inversion  is  sometimes  called 
looming.  Sometimes  objects  entirely  below  the  horizon  arg 
elevated  by  refraction  sufficiently  to  appear  distinctly  above  the 
horizon. 

448.  The  Rainbow.  —  The  rainbow,  when  complete,  is 
a  colored  arc  having  a  radius  of  about  41°,  and  containing  all 
the  prismatic  hues,  the  red  being  on  the  outside  and  the  violet 
on  th:  insid:.  There  is  often  a  second  fainter  bow,  with  its 
colors  in  the  reverse  order,  outside  of  the  primary  bow.  This 
is  called  the  secondary  bow.  Occasionally,  there  are  one 
or  more  supernumerary  bows  within  the  primary  bow,  com- 
posed of  colored  arcs  of  greater  or  less  extent. 

The  rainbow  appears  whenever  the  sun  shines  upon 
falling  rain  in  the  opposite  part  of  the  heavens.  The  bow 
is  never  seen  unless  the  sun  is  within  41°  of  the  horizon, 
and  the  nearer  the  sun  is  to  the  horizon  the  larger  the  arc 
of  the  bow. 

A  line  drawn  from  the  sun  through  the  eye  of  the  observer 
points  to  the  centre  of  the  circle  of  which  the  rainbow  is  a  part, 
and  is  called  the  axis  of  the  bow.  A  line  drawn  from  the  eye 
of  the  observer  to  the  centre  of  the  colored  band  at  any  point 
makes  an  angle  of  about  41°  with  the  axis  of  the  bow.  A  Hne 
drawn  from  the  eye  of  the  observer  to  the  red  edge  of  the  bow 
makes  an  angle  of  about  42*4°  with  this  axis  ;  and  one  drawn  to 
the  violet  edge,  an  angle  of  about  40^4°. 

The  rainbow  is  produced  by  rays  of  sunlight  reflected  from 
the  rear  surface  of  the  rain-drops.  These  rays  would  be  refracted 
both  on  entering  and  leaving  the  drops.  At  each  refraction 
they  would  be  bent  towards  a  line  drawn  to  the  point  of  contact 


302 


ELEMENTS    OF 


Fig.  341- 


of  the  ray  with  the  rear  surface  of  the  drop,  and  parallel  with 
the  incident  ray  of  sunlight,  and  therefore  parallel  with  the  axis 
of  the  bow  (Figure  341).  At  an 
angle  of  41°  with  the  axis  of  the 
bow  the  rays  emerge  from  the  rain- 
drop crowded  together  and  almost 
parallel  wrth  each  other  (Figure 
342).  These  rays  are  able  to  pre- 
serve their  intensity  through  long 
atmospheric  distances.  At  all  other 
angles  the  emergent  rays  are  divergent,  and  become  too  feeble 
to  affect  the  eye.  Accordingly,  whenever  the  observer  looks 
41°  away  from  the  axis  of  the  bow,  his  eye  catches  some  of 

Fig-  342. 


these  nearly  parallel  rays  which  are  emerging  from  some  rain- 
drop. He  therefore  sees  a  bright  band,  circular  in  form,  and 
having  a  radius  of  41°. 

The  different  colored  rays  are  refracted  unequally  on  their 
passage  through  the  rain-drop ;  hence  the  angle  of  parallelism 
is  somewhat  different  for  different  colors,  being  about  42^°  for 
the  red  and  about  4o>£0  for  the  violet.  This  accounts  for  the 
colors  of  the  rainbow,  the  violet  rays  reaching  the  eye  from 
drops  nearer  the  axis  than  those  which  send  red  rays  to  the  eye. 


NATURAL    PHILOSOPHY. 


303 


No  two  observers  see  the  same  rainbow  ;  that  is  to  say,  no  two 
eyes  receive  the  colors  from  the  same  set  of  rain-drops. 

Fig.  343« 


The  secondary  bow  is  produced  by  rays  that  have  suffered 
two  reflections  within  the  rain-drops  (Figure  343).  Figure 
344  shows  the  relative  position  of  the  two  bows. 

Fig.  344. 


B.   REFLECTION. 

449.   Diffused  Daylight.  —  When  the  sun  shines  upon 

any  portion  of  the  atmosphere,  the  particles  of  air  reflect 

the  rays  of  light  irregularly,   and  so   scatter  the   light  in 


304  ELEMENTS    OF 

every  direction,  thus  giving  rise  to  diffused  daylight.  Were 
it  not  for  the  atmosphere,  shadows  would  be  utterly  devoid 
of  light,  and  rooms  into  which  the  sun  was  not  directly 
shining  would  be  totally  dark. 

450.  Twilight.  —  Were   it  not  for  the  atmosphere,  the 
darkness   of  midnight  would   begin   the  moment  the  sun 
sank  below  the  horizon,  and  would  continue  till  he  rose 
again  above  the  horizon  in  the  east,  when  the  darkness  of 
the  night  would  be  suddenly  succeeded  by  the  full  light  of 
day.     The  gradual  transition  from  the  light  of  day  to  the 
darkness  of  the  night,  and  from  the  darkness  of  the  night 
to  the  light  of  day,   is  called  twilight,  and  is  due  to  the 
diffusion  of  light  from  the  upper  layers  of  the  atmosphere 
after  the  sun  has  ceased  to  shine  on  the  lower  layers  at 
night,  or  before  it  has  begun  to  shine  upon  them  in  the 
morning. 

Twilight  begins  and  ends  when  the  sun  is  about  18° 
below  the  horizon. 

451.  Color  of  the  Sky.  —  Large  particles  reflect  and  diffuse 
all  luminous  waves  equally  well,  but  a  particle  intermediate  in 
size  between  a  red  and  a  violet  wave  would  reflect  a  greater 
proportion  of  violet  waves  than  of  red  waves.     The  smaller  the 
particles  suspended  in  a  transparent  medium,  the  greater  the 
proportion  of  blue  rays  reflected  and  the  less  the  proportion  of 
red.     Hence  any  transparent  medium  holding  very  minute  parti- 
cles of  any  kind  in  suspension  will  appear  blue  in  reflected  ligjjt. 
According  to  Tyndall,  the  sky  owes  its  blue  color  to  the  minute 
particles  of  watery  vapor  or  other  substances  suspended  in  it. 
The  more  minute  the  particles,  the  bluer  the  sky.     As  we  ap- 
proach the  horizon  the  sky   inclines   to  white,  because  of  the 
larger  particles  which  are  present  in  the  lower  layers  of  the 
atmosphere. 

When  the  sun  is  near  the  horizon,  the  rays  traverse  a  greater 
atmospheric  distance,  and  the  separation  between  the  long  and 
short  waves  is  more  complete.  In  this  case  the  rays  which 
reach  us,  and  which  illumine  the  clouds  and  the  lower  portion  of 
the  sky,  are  those  which  are  allowed  to  pass  the  particles,  and 


NATURAL    PHILOSOPHY. 


3°5 


not  those  which  are  reflected  by  them.  Hence  the  evening  sky 
inclines  to  yellow,  orange,  or  red,  according  as  the  shorter  waves 
have  been  more  or  less  completely  turned  back.  Unless  there 
are  clouds  in  the  upper  portions  of  the  sky,  these  colors  are 
limited  to  the  regions  near  the  horizon,  since  it  is  there  only  that 
the  particles  in  the  air  are  large  enough  to  reflect  the  larger 
waves  transmitted  to  them. 

C.    COROX^E  AND  HALOS. 

452.  Corona.  —  When  light  fleecy  clouds  pass  over  the  sun 
or  moon,  one  or  more  iris-colored  rings  are  often  seen  about 
these  bodies,  the  inner  ring  being  from  3°  to  6°  in  diameter. 
The  blue  edges  of  these  rings  are  towards  the  sun  or  moon,  and 
the  red  edges  away  from  it.  These  rings  are  called  coronce. 
They  are  more  frequently  noticed  about  the  moon  than  about 
the  sun,  owing  to  the  dazzling  brilliancy  of  the  latter.  They  are 
shown  at  the  centre  of  the  lower  part  of  Figure  345. 

Fig-  345- 


453.  ^Halos.  —  Halos  are  circles  formed  around  the  sun  or 
moon.     When  bright  they  are  seen  to  be  composed  of  the  pris- 

20 


306  ELEMENTS    OF 

matic  colors.  Thay  are  larger  than  corona,  and  are  red  on  the 
edge  towards  the  sun.  The  halo  most  often  seen  has  a  radius 
of  22°.  This  is  shown  at  h  h  (Figure  345).  A  second  halo  is 
sometimes  formed  having  a  radius  of  46°,  H  H  ;  and  occasion- 
ally a  third  halo  is  seen  having  a  radius  of  about  90°,  ff  //'. 

454.  Parhelic  Circle.  —  When  a  halo  is  formed  around  the 
sun  we  often  notice  a  white  circle  passing  through  the  sun  and 
parallel  to  the  horizon  (Figure  345).     This  is  called  a  parhelic 
circle.     It  never  exhibits  prismatic  colors  like  the  first-men- 
tioned halos. 

455.  Parhelia.  —  Near  the  points  where  halos  cut  the  par- 
helic circle  there  is  a  double  cause  of  light,  and  here  the  illumi- 
nation is  sometimes  so  great  as  to  present  the  appearance  of  a 
mock  sun,  p p  and  P  P  (Figure  345),  and  is  called  a  parhelion. 
Parhelia  are  generally  red  on  the  side  which  is  toward  the  sun, 
and  they  sometimes  have  a  prolongation  in  the  form  of  a  tail 
several  degrees  in  length,  whose  direction  coincides  with  that 
of  the  parhelic  circle. 

456.  Contact  Arches.  — Arcs  of  colored  circles  with  variable 
curvatures  are  sometimes  seen  touching  the  halos  of  22°  and 
46°  at  their  highest  and  lowest  points,  a,  b  (Figure  345).     Some- 
times we  notice  two  arcs  of  circles  nearly  white,  A,  intersecting 
the  parhelic  circle  at  a  point  directly  opposite  to  the  sun,  and 
inclined  to  this  circle  at  angles  of  about  6^°. 

457.  Vertical  Columns  passing  through  the  Sun.  —  Some- 
times, near  sunset,  we  notice  a  luminous  column  perpendicular 
to  the  horizon,  rising  from  the  sun  to  the  height  of  10°  or  15°, 
and  occasionally  still  higher.-    Sometimes  a  little  before  sunset, 
a   similar  column  of    light  is   seen  to   shoot   down   from   the 
sun  toward  the  horizon.     Sometimes  columns  are  seen  simul- 
taneously both  above  and  below  the  sun  ;  and  if  the  halo  of  22° 
is  seen  at  the  same  time,  this  column,  together  with  the  parhelic 
circle,  presents  the  appearance  of  a  rectangular  cross  within  the 
halo  (Figure  345). 


NATURAL    PHILOSOPHY.  307 

VIII. 

THE   THREE  GREAT   CIRCULATIONS   OF   THE 
GLOBE. 

458.  The  Atmospheric   Circulation.  —  In   the  atmospheric 
circulation,  which  gives  rise  to  the  various  systems  of  winds, 
masses  of  air  are  kept  moving  round  and  round.     This  circu- 
lation is  maintained  by  heat  received  from  the  sun,  and  absorbed 
by  the  atmosphere.     The  heat  thus  absorbed  causes  the  air  to 
expand,  rise,  and  overflow,  while  gravity  pulls  the  colder  and 
heavier  air  down  and  around  to  supply  its  place.     The  mechani- 
cal energy  of  the  moving  masses  of  air  is  exactly  equal  to  the 
energy  of  the  solar  radiations  consumed  in  maintaining  the 
motion.     The  energy  of  the  solar  radiations  absorbed  by  the 
air  is  transformed  by  expansion  into  the  mechanical  energy  of 
the  winds.      Winds  a»e  merely  transmuted  sunshine. 

459.  The  Aqueous  Circulation.  —  In  the  aqueous  circulation, 
water  is  continually  passing  into  the  atmosphere  as  vapor,  then 
falling  from  the  atmosphere  as  rain,  and,  finally,  running  in 
various  streams  down  to  the  level  of  the  ocean.     This  circula- 
tion is  also  maintained  by  energy  absorbed  from  solar  radiations. 
The  solar  heat  absorbed  by  water  converts  it  into  vapor,  and 
raises  it  into  the  atmosphere.     When  this  vapor  condenses  in 
the  atmosphere,  gravity  draws  it  to  the  surface  of  the  earth,  and 
to  the  level  of  the  ocean.     In  the  evaporation  of  the  water  the 
kinetic  energy  of  the   solar  radiations   is   converted   into   the 
potential  energy  of  molecular  seplration,  and  in  the  expansion 
by  which  this  vapor  is  raised  into  the   atmosphere,  into  the 
potential  energy  of  mechanical  separation.     In  the  condensation 
of  the  vapor  in  the  atmosphere,  its  potential  energy  of  molecular 
separation  is  transformed  into  the  kinetic  energy  of  heat,  and  in 
the  fall  of  the  rain  to  the  earth  and  the  descent  of  the  water  to 
the  sea,  its  potential  energy  of  mechanicnl  separation  is  trans- 
formed  into  the  kinetic  energy  of  mechanical  motion.      The 
energy   of  the   mountain  stream  which  drives    the   mill   came 
originally  to  the   earth  in  the  minute  vibrations  of  the  solar 
radiations,  and  was  absorbed  from  these  by  water  and  air. 

460.  The  Circulation  of  Carbon.  —  Carbon  exists  in  the  at- 


308  ELEMENTS    OF    NATURAL    PHILOSOPHY. 

mosphere  in  carbonic  acid  gas,  a  compound  of  carbon  and 
oxygen.  This  gas  is  absorbed  from  the  atmosphere  by  leaves 
of  plants,  in  which  it  is  decomposed  by  solar  radiations,  which 
are  also  absorbed  by  the  leaves.  The  carbon  is  retained  by  the 
plant,  and  the  oxygen  is  restored  to  the  atmosphere.  When 
vegetable  substances  are  consumed  by  the  natural  process  of 
decay,  or  as  food  in  the  bodies  of  animals,  or  as  fuel  in  our 
stoves  and  furnaces,  the  carbon  again  unites  with  the  oxygen 
and  forms  carbonic  acid,  whrh  passes  back  into  the  atmosphere. 
Thus  carbon  is  kept  going  round  and  round,  from  the  atmos- 
phere to  plants  and  animals,  and  back  again  into  the  atmosphere. 

This  circulation,  like  the  other  two,  is  maintained  by  energy 
obtained  from  solar  radiations.  By  the  decomposition  of  the 
carbonic  acid  in  the  leaves  of  the  plant,  the  kinetic  energy  of 
the  sunbeam  is  transformed  into  the  potential  energy  of  chemical 
separation  ;  and  in  the  consumption  of  food  and  fuel,  the  po- 
tential energy  thus  required  by  carbon  is  converted  into  kinetic 
energy  again.  Animals  derive  all  their  energy  from  the  food 
which  they  eat,  and  as  this  food  is  consumed  in  the  body,  its 
potential  energy  is  converted  partly  into  the  kinetic  energy  of 
heat,  and  partly  into  the  kinetic  energy  of  mechanical  motion. 
The  energy  employed  by  man  in  thinking,  writing,  speaking,  or 
in  doing  any  kind  of  work  whatever,  came  to  the  earth  originally 
from  the  sun  in  the  minute  vibrations  of  the  ether. 

Coal  is  a  vegetable  substance,  and  its  potential  energy  has 
been  derived  from  solar  radiations ;  and  when  we  burn  coal  for 
fuel  or  coal  gas  for  light,  we  are  simply  extracting  from  the  coal 
the  sunbeams  that  were  ages  ago  absorbed  by  the  leaves  of 
plants  and  transformed  into  the  potential  energy  of  chemical 
separation. 

461.  Source  of  Terrestrial  Energy.  —  Nearly  every  form  of 
terrestrial  energy  is  derived  from  the  sun  and  comes  to  the 
earth  in  the  solar  radiations.  The  three  chief  agents  for  ab- 
sorbing this  energy  and  transforming  it  into  a  kind  adapted  for 
our  use  are  water,  air,  and  leaves  of  plants. 


INDEX. 


Aberration  chromatic,  170. 
spherical,  170. 
Action  and  reaction,  7. 
Affinity,  3,  7. 

Air-chamber  in  pumps,  84. 
Air,  pressure  of,  67. 
Air-pump,  the,  65. 
Ampere's  rule,  222. 
Anion,  the,  232. 
Anode,  the,  232. 
Aqueous  circulation,  the,  307. 
Archimedes's  principle,  58. 
Artesian  wells,  74. 
Astatic  galvanometer,  223. 

needle,  223. 
Astronomy,  4 
Atmosphere,  circulation  in,  307. 

composition  of,  257. 

condensation  in,  277. 

electricity  in,  292. 

height  of,  257. 

humidity  of,  268. 

movements  of,  270. 

reflection  in,  303. 

refraction  in,  298. 

temperature  of,  260. 

weight  of,  258. 
Atoms,  i. 
Aurora,  the,  296. 
Avogadro's  law,  64. 


Balance,  the,  29. 

Balance-wheel,  compensation,  117. 

B  illoons,  60. 

Barometer,  the,  81,  258. 

Beam,  denned,  152. 

Beats,  musical,  103. 

Be'l's  telephone,  237. 

Boiling,  127. 

Brocken,  the  spectre  of  the,  183. 

Bunseii's  cell,  228. 


Calorimeters,  132. 

Camera  obscura,  the,  177. 

Capillarity,  76. 

Capstan,  the,  49. 

Carbon,  circulation  of,  308. 

Cathode,  the,  232. 

Cation,  the,  232 

Centre  of  gravity,  23. 

Lentrifugal  force,  9. 

Centripetal  force,  10. 

C.  G.  S.  system,  13. 

Charles's  law,  65. 

Chemistry,  4- 

Climates,  marine  and  continental,  265 

Clocks,  37. 

Clouds,  281. 

Cog-wheels,  48. 

Cohesion,  3,  53. 

Coil,  the  induction,  240. 

Collision  of  elastic  bodies,  16. 

Color-blindness,  190. 

Color  chart,  the,  186. 

of  the  sky,  304. 

scale,  187. 

Color-disc,  the  ideal,  186. 
Colors,  complementary,  186 
from  absorption,  190. 
primary,  187. 
Condensation,  129. 
Congelation,  124. 
Contact-arches,  306. 
Coronae,  305. 

Cottrell's  straw  electroscope,  204. 
Cryophorus,  the,  135. 
Crystals,  90. 
Cyclones,  291. 


D. 

Daniell's  cell,  228. 
Daylight,  diffused,  303. 
Density,  6. 
Dew,  origin  of,  277. 
Dew-point,  the,  260. 
Diathermanous  bodies,  145. 


INDEX. 


Dielectrics,  208. 
Discharge,  auroral,  218. 

brush,  220. 

electrical,  217. 

glow,  219. 

spark,  217. 
Distillation,  129. 
Dynamo-electric  machines,  242. 
Dyne,  defined,  13. 


Ear,  the  human,  112. 
Ear-trumpet,  the,  100. 
Ebullition,  127. 
Echoes,  99. 

Edison's  electric  lamp,  253. 
phonograph,  109. 
telephone,  238. 
Elasticity,  3,  91. 
Electrical  attraction,  202,  209. 
charge,  2»o. 
conductors,  204,  224. 
discharge,  217. 
excitation,  201. 
induction,  205. 
insulators,  205. 
machine,  212. 
potential,  209. 
repulsion,  202,  209. 
resistance,  225. 
Electric  carrier,  the,  207. 
current,  221. 
illumination,  253. 
mill,  214. 
wind,  213 

Electricity,  atmospheric,  292. 
frictional,  201. 
thermal,  252. 
two  kinds  of,  203. 
velocity  of,  226. 
voltaic,  221. 

Electro-chemical  action,  226. 
Electro-dynamics,  221. 
Electro-kinetics,  221. 
Electrolysis,  232. 
Electro-magnetic  induction,  234. 
Electro-magnets,  235 
Electro-metallurgy,  233. 
Electrometers,  210. 
Electromotive  force,  224. 
Electro-motors,  251. 
Electrophorus,  the,  206. 
Electroplating,  234. 
Electroscope,  Cottrell's,  204. 
gold-leaf,  206. 
Electro-statics,  221. 
Electro-thermal  action,  252. 
Electrotyping,  233. 
Energy,  defined,  18. 
kinetic,  19. 
potential,  19. 
source  of  terrestrial,  308. 
Equilibrium,  25. 

of  floating  bodies,  60. 
Erg,  defined,  18. 
Ether,  the,  2, 149. 


Evaporation,  125. 

latent  heat  of,  126. 
Expansion,  latent  heat  of,  134. 
Eye,  the  human,  178. 
Eyes,  old,  185. 


F. 


Falling  bodies,  30. 

Faraday's  liquefaction  of  gases,  137. 

nomenclature  of  electrolysis, 

232. 

Far-sightedness,  184. 
Floating  bodies,  60. 
Fluids,  c5. 
Fluorescence,  191. 
Fog,  279. 

Foot-poundal,  defined,  18. 
Force,  defined,  7. 

impulse  of,  13. 

units  of,  12. 
Force-pump,  the,  83. 
Forces,  composition  of,  20. 

parallelogram  of,  20. 

resolution  of,  20,  22. 

the  three  great,  3. 
Fountain  in  vacuo,  80. 
Franklin's  experiment,  128. 
Freezing  mixtures,  136. 
Frost  in  valleys,  278. 
Fusing-point,  the,  123. 
Fusion,  123. 

latent  heat  of,  124. 


G. 

Galvanometer,  the,  223. 

astatic,  223. 
Gases  and  vapors,  126. 

cohesion  in,  54. 

conductivity  of,  142. 

diffusion  of,  63 

expansibility  of,  63. 

expansion  of,  118. 

laws  of.  64. 

solidification  of,  137. 
Gold-leaf,  92. 
Graham's  pendulum,  117. 
Gravitation  units,  12. 
Gravity,  3. 

centre  of,  23. 
law  of,  23. 
Grove's  cell,  228. 


H. 

Hail,  286. 
Halos,  305. 

Harrison's  pendulum,  116. 
Heat,  absorption  of,  146. 
and  work,  134. 
conduction  of,  139. 
consumed  in  evaporation,  135. 
expansion,  134. 
liquefaction,  135. 


INDEX. 


Heat ,  convection  of,  142,  143- 

developed  by  electricity,  252. 

distribution  of,  139. 

effects  of,  114. 

expansion  by,  114. 

latent,  -124. 

measurement  of,  131. 

mechanical  equivalent  of,  138. 

radiation  of,  143. 

specific,  131. 

unit  of,  131. 
Hoar-frost,  278. 
Holtz  electrical  machine,  216. 
Hot- houses,  148. 
Hydraulic  press,  the,  56. 

tourniquet,  the,  88. 
Hydrometers,  62. 
Hydrometer,  tlie,  268. 

Mason's,  268. 
Hygroscope,  the,  268. 


Illumination,  155. 

Images,  formed  by  lenses,  168. 

from  small  apertures,  152. 

in  concave  mirrors,  172. 

in  convex  mirrors,  173. 

in  plane  mirrors,  157. 

multiple,  157. 
Inclined  plane,  the,  50. 
Indian  summer,  280. 
Induction  coils,  240. 
Inertia,  8. 
Ions,  232. 
Irradiation,  181. 


Kaleidoscope,  the,  158. 


Land  and  sea  breezes,  276. 
Lantern  for  projection,  177. 
I  eclanche  cell,  229. 
Lenses,  achromatic,  171. 

axes  and  foci  of,  166. 
forms  of,  165. 
images  formed  by,  168. 
magnifying  power  of,  169. 
Lever,  the,  42. 

compound,  43. 
Leyden  jar,  the,  214 
Light,  diffusion  of,  15^ 
dispersion  of,  161. 
radiation  of,  149. 
reflection  of,  156. 
refraction  of,  158. 
total  reflection  of,  160. 
velocity  of,  150. 
Lightning,  293. 
Lightning-rods,  293. 
Liquid^  cohesion  in,  ^4. 

compressibility  of,  69. 


Liquids,  conductivity  of,  141- 
elasticity  of,  70. 
evaporation  of,  125- 
expansion  of,  117. 
pressure  of,  70. 
volatile,  125. 

Lodestone,  the,  192. 


M. 

Machines,  39. 

Magdeburg  hemispheres,  67. 
Magnetic  force,  lines  of,  193. 
induction,  194. 
needles,  197,  221. 
Magnetism,  192. 

terrestrial,  197. 

Magnetization  of  steel  bars,  195. 
Magnets,  192. 
Magneto-electric  currents,  235. 

machines,  242. 
Mariner's  compass,  the,  199. 
Mariotte's  law,  64 
Mason's  hygrometer,  268. 
Matter,  constitution  of,  i. 

properties  of,  4. 

three  states  of,  53. 
Mechanical  powers,  39. 
Melting-point,  the,  123. 
Metals,  conductivity  of,  141. 
Meteorology,  257. 
Metre,  the,  5. 
Metric  system,  the,  5. 
Microphone,  the,  240. 
Microscope,  simple,  173. 

compound,  173. 
Mirage,  299. 
Mirrors,  concave,  171. 

convex,  172. 

plane,  157. 
Mist,  279. 
Molecules,  i. 
Momentum,  13. 
Monsoons,  275. 
Motion,  atomic,  3. 

molar,  3. 

molecular,  3,  53. 

parallelogram  of,  15. 
Musical  instruments,  106. 


N. 

Natural  philosophy,  4. 
Near-sightedness,  184. 
Newton's  first  law  of  motion,  7. 

second  law  of  motion,  13. 

third  law  of  motion,  16. 
Nickel-plating,  234. 
Nodal  lines,  95. 
Noise,  102. 


O. 

Ohm,  the,  225. 
Opaque  bodies,  153. 


312 


INDEX. 


Opera-glass,  the,  175. 
Optical  axis,  the,  181. 
Organ  pipes,  107. 


P. 

Papin's  digester,  128. 
Parachute,  the,  60. 
Parhelia,  306. 
Parhelic  circle,  306. 
Pascal's  experiment,  81. 

law,  55. 

vessels,  71. 
Pendulum,  the,  36. 
Pendulums,  compensating,  116. 
Penumbra  of  shadow,  154. 
Phonograph,  the,  109. 
Phosphorescence,  191. 
Photometry,  155. 
Physical  sciences,  the,  4. 
Physics,  4. 
Pores,  2. 

Position  of  advantage,  19. 
Potential,  electrical,  209. 
Poundal,  defined,  12. 
Prisms,  achromatic,  162. 

direct-vision,  162. 
Pulley,  the,  45. 
Pyrometers,  122. 


R. 

Radiation,  theory  of,  145. 
Radiations,  luminous,  145. 

obscure,  145. 
Rain,  origin  of,  285. 
Rainbow,  the,  301. 
Ray,  defined,  152. 
Reaction,  7. 
Reflection,  total,  160. 
Relay,  the,  246. 
Resonance,  104. 
Rumford's  photometer,  156. 


S. 

Screw,  the,  51. 

endless,  52. 
Shadows,  153. 
Singing  flames,  109. 
Siphon,  the,  85. 
Saow  crystals,  286. 

line  of  perpetual,  267. 

origin  of,  285. 
Solids,  cohesion  in,  53. 

crystalline,  90. 

expansion  of,  114. 

properties  of,  91. 
Sonometer,  the,  106. 
Sound,  intensity  of,  98. 

interference  of,  102. 

origin  of,  93. 

pitch  of,  101. 

propagation  of,  96. 

quality  of,  101. 


Sound,  reflection  of,  99. 
velocity  of,  99. 
waves,  97. 

Sounding-boards,  105. 
Spangled  pane,  the,  218 
Speaking-trumpet,  the,  100. 
Specific  gravity,  29,  61. 
Spectroscope,  the,  163. 
Spectrum  analysis,  164. 

bright-lined,  164. 

continuous,  164. 

dispersion,  161. 

reversed,  164. 
Spheroidal  state,  130. 
Spirit-level,  the,  75. 
Springs,  74. 

Stability  of  rotation,  n. 
Steam-engine,  the,  138. 
Steam,  latent  heat  of,  133. 
Stereoscope,  the,  183. 
Storms,  287. 
Strain,  defined,  3. 
Stress,  defined,  3,  7. 
Stringed  instruments,  106. 
Substance,  i. 
Suction-pump,  the,  82. 


T. 

Tantalus's  cup,  86. 
Telegraph  key,  the,  242. 
Morse's,  242. 
register,  245. 
relay,  246. 
sounder,  244. 
terminal  stations,  247. 
way  station,  249. 
Telegraphy,  242. 
Telephone,  Bell's,  237 

Edison's,  238. 
Telescope,  the,  174. 

reflecting,  176. 
terrestrial,  175. 
Temperature,  119. 

absolute,  65. 

Thermo-electric  piles,  252. 
Thermometer,  alcohol,  122. 

differential,  122,  252. 
mercurial,  119. 
scales,  120. 
Thermopile,  the,  252. 
Thunder,  295. 
Torricelli's  experiment,  80. 
Transparent  bodies,  153. 
Turbine  wheel,  the,  89. 
Twilight,  304. 


U. 

Umbra  of  shadow,  154. 
Unison,  101. 
Units,  English,  5. 

French,  5. 

gravitation,  12. 

material,  3. 

mechanical,  5. 


INDEX. 


3r3 


Units  of  force,  n. 
of  work,  1 8. 


V. 


Vapors,  126,  129. 
Velocity,  6. 

Vibrations,  fundamental,  94. 
harmonic,  96. 
sympathetic,  104. 
Visual  angle,  the,  181. 
Voice»  the  human,  109. 
Volt,  the,  225. 
Voltaic  battery,  the,  229. 
arc,  the,  254. 
cell,  the,  226. 

bichromate  of  potash,  228. 
Bunsen's,  228. 
Daniell's,  228. 
Grove's,  228. 
Leclanche,  229. 
zinc  and  copper,  226. 
cells,  two-fluid,  227. 
Voltameter,  the,  232. 


W. 

Water,  expansion  of,  118. 

latent  heat  of,  132. 
Water-wheels,  86. 
Weber,  the,  225. 
Wedge,  the,  50. 
Weight,  denned,  28. 
Wheel  and  axle,  the,  47. 
Wheels,  belted,  49. 
Wind  instruments,  107. 
Windlass,  the,  49. 
Winds,  270. 

cause  of,  272. 

middle-latitude,  2 74, 

polar,  275. 

systems  ot,  273. 

trade,  274- 

Work,  defined,  17. 

units  of,  18. 


Z 


Zoetrope,  the,  180. 


ib 


r 


541753 


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